bayesian sensitivity analysis for unmeasured confounding in observational studies we consider bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure binary response measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models a model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder simulation from the posterior distribution is accomplished using markov chain monte carlo because the model for unmeasured confounding is not identifiable standard large sample theory for bayesian analysis is not applicable consequently the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown using simulations we investigate the coverage probability when averaged with respect to various distributions over the parameter space the results indicate that credible intervals will have approximately nominal coverage probability on average when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies we motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure

sample average approximation for the continuous type principal agent problem abstract we develop a method for finding approximate solutions to the continuous agent type principal agent problem when analytical methods are not available the solution is calculated by solving a discrete agent type version of the problem using sample average approximation and bootstrapping we show how a solution to the approximate problem can be used to derive a lower bound and expected upper bound for the optimal objective function and evaluate the error associated with the approximation numerical examples illustrate convergence in the approximate solution to the true solution as the number of samples increases this works yields a method for obtaining some tractability in continuous type principal agent problems where solutions were previously unavailable

algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

the additivity of traces in triangulated categories abstract we explain a fundamental additivity theorem for euler characteristics and generalized trace maps in triangulated categories the proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation the refinement consists of several new axioms relating products and distinguished triangles the axioms hold in the examples and shed light on generalized homology and cohomology theories

case control studies assessing the effect of a confounding factor summary upper and lower bounds for the strength of the effect of a dichotomous confounding factor on the exposure disease relationship are developed for case control studies of a a problem in the design and analysis of a case control study is the identification of confounding factors controversies frequently arise about whether an exposure disease relationship is spurious i e caused by extraneous or confounding factors that were not measured or controlled as part of the study the effect of confounding factors has been discussed quantitatively by bross 1966 and schlesselman 1978 in this paper we develop upper and lower bounds for the stratum specific odds ratios which are applicable for assessing the effect of a confounding factor we restrict our attention to the simple case involving a dichotomous disease variable denoted by d if present and d if absent a dichotomous exposure variable denoted by e if present and e if absent and a single dichotomous extraneous factor f with f1 and fo denoting its two levels 2 bounds we parameterize the joint distributions of e and f in d and d as follows

comodules and landweber exact homology theories abstract we show that if e is a commutative mu algebra spectrum such that e is landweber exact over mu then the category of e e comodules is equivalent to a localization of the category of mu mu comodules this localization depends only on the heights of e at the integer primes p it follows for example that the category of e n e n comodules is equivalent to the category of v n 1 bp v n 1 bp comodules these equivalences give simple proofs and generalizations of the miller ravenel and morava change of rings theorems we also deduce structural results about the category of e e comodules we prove that every e e comodule has a primitive we give a classification of invariant prime ideals in e and we give a version of the landweber filtration theorem

quotients of absolute galois groups which determine the entire galois cohomology for a prime power q pd and a field f containing a root of unity of order q we show that the galois cohomology ring h g f mathbb z q is determined by a quotient g f 3 of the absolute galois group gf related to its descending q central sequence conversely we show that g f 3 is determined by the lower cohomology of gf this is used to give new examples of pro p groups which do not occur as absolute galois groups of fields

artin tate motivic sheaves with finite coefficients over an algebraic variety we propose a construction of a tensor exact category fxm of artin tate motivic sheaves with finite coefficients z m over an algebraic variety x over a field k of characteristic prime to m in terms of etale sheaves of z m modules over x among the objects of fxm in addition to the tate motives z m j there are the cohomological relative motives with compact support mccm y x of varieties y quasi finite over x exact functors of inverse image with respect to morphisms of algebraic varieties and direct image with compact supports with respect to quasi finite morphisms of varieties y x act on the exact categories fxm assuming the existence of triangulated categories of motivic sheaves dm x z m over algebraic varieties x over k and a weak version of the six operations in these categories we identify fxm with the exact subcategory in dm x z m consisting of all the iterated extensions of the tate twists mccm y x j of the motives mccm y x an isomorphism of the z m modules ext between the tate motives z m j in the exact category fxm with the motivic cohomology modules predicted by the beilinson lichtenbaum etale descent conjecture recently proved by voevodsky rost et al holds for smooth varieties x over k if and only if the similar isomorphism holds for artin tate motives over fields containing k when k contains a primitive m root of unity the latter condition is equivalent to a certain koszulity hypothesis as shown in our previous paper positselski mixed artin tate motives with finite coefficients mosc math j 11 2011 317 402

morita theory for hopf algebroids and presheaves of groupoids comodules over hopf algebroids are of central importance in algebraic topology it is well known that a hopf algebroid is the same thing as a presheaf of groupoids on aff the opposite category of commutative rings we show in this paper that a comodule is the same thing as a quasi coherent sheaf over this presheaf of groupoids we prove the general theorem that internal equivalences of presheaves of groupoids with respect to a grothendieck topology t on aff give rise to equivalences of categories of sheaves in that topology we then show using faithfully flat descent that an internal equivalence in the flat topology gives rise to an equivalence of categories of quasi coherent sheaves the corresponding statement for hopf algebroids is that weakly equivalent hopf algebroids have equivalent categories of comodules we apply this to formal group laws where we get considerable generalizations of the miller ravenel and hovey sadofsky change of rings theorems in algebraic topology

hz algebra spectra are differential graded algebras we show that the homotopy theory of differential graded algebras coincides with the homotopy theory of h algebra spectra namely we construct quillen equivalences between the quillen model categories of unbounded differential graded algebras and h algebra spectra we also construct quillen equivalences between the differential graded modules and module spectra over these algebras we use these equivalences in turn to produce algebraic models for rational stable model categories we show that basically any rational stable model category is quillen equivalent to modules over a differential graded algebra with many objects

the group of k1 zero cycles on the second generalized severi brauer variety of an algebra of index 4 abstract in this manuscript it is shown that the group of k 1 zero cycles on the second generalized severi brauer variety of an algebra a of index 4 is given by elements of the group k 1 a together with a square root of their reduced norm utilizing results of krashen concerning exceptional isomorphisms we translate our problem to the computation of cycles on involution varieties work of chernousov and merkurjev then gives a means of describing such cycles in terms of clifford and spin groups and corresponding r equivalence classes we complete our computation by giving an explicit description of these algebraic groups

sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures robins introduced marginal structural models msms and inverse probability of treatment weighted iptw estimators for the causal effect of a time varying treatment on the mean of repeated measures we investigate the sensitivity of iptw estimators to unmeasured confounding we examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user specified function we present augmented iptw estimators of msm parameters and prove their consistency for the causal effect of an msm assuming a correct confounding bias function for unmeasured confounding we apply the methods to assess sensitivity of the analysis of hernan et al who used an msm to estimate the causal effect of zidovudine therapy on repeated cd4 counts among hiv infected men in the multicenter aids cohort study under the assumption of no unmeasured confounders a 95 per cent confidence interval for the treatment effect includes zero we show that under the assumption of a moderate amount of unmeasured confounding a 95 per cent confidence interval for the treatment effect no longer includes zero thus the analysis of hernan et al is somewhat sensitive to unmeasured confounding we hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications

zeta functions of regular arithmetic schemes at s 0 lichtenbaum conjectured in 22 the existence of a weil etale cohomology in order to describe the vanishing order and the special value of the zeta function of an arithmetic scheme x at s 0 in terms of euler poincare characteristics assuming the conjectured finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over spec z in particular we compute uncon ditionally the right weil etale cohomology of number rings and projective spaces over number rings we state a precise version of lichtenbaum s con jecture which expresses the vanishing order resp the special value of the zeta function x s at s 0 as the rank resp the determinant of a single perfect complex of abelian groups r w c x z then we relate this conjecture to soule s conjecture and to the tamagawa number conjecture lichtenbaum s conjecture for projective spaces over the ring of integers of an abelian number field follows

reconstructing function fields from rational quotients of mod ell galois groups in this paper we develop the main step in the global theory for the mod ell analogue of bogomolov s program in birational anabelian geometry for higher dimensional function fields over algebraically closed fields more precisely we show how to reconstruct a function field k of transcendence degree ge 5 over an algebraically closed field up to inseparable extensions from the mod ell abelian by central galois group of k endowed with the collection of mod ell rational quotients

triple massey products of weight 1 n 1 in galois cohomology abstract fix an arbitrary prime p let f be a field containing a primitive p th root of unity with absolute galois group g f and let h n denote its mod p cohomology group h n g f z p z the triple massey product abbreviated 3mp of weight n k m n 3 is a partially defined multi valued function h n h k h m h n k m 1 in this work we prove that for an odd prime p any defined 3mp of weight 1 k 1 contains zero

the six operations in equivariant motivic homotopy theory abstract we introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks x g where g is a linearly reductive linear algebraic group we extend to this equivariant setting the main foundational results of motivic homotopy theory the unstable purity and gluing theorems of morel voevodsky and the stable ambidexterity theorem of ayoub our proof of the latter is different than ayoub s and is of interest even when g is trivial using these results we construct a formalism of six operations for equivariant motivic spectra and we deduce that any cohomology theory for g schemes that is represented by an absolute motivic spectrum satisfies descent for the cdh topology

assessing the sensitivity of regression results to unmeasured confounders in observational studies this paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variable after adjusting for measured covariates the proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders one can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable under certain conditions there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model one can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports the proposed method handles both binary response and censored survival time data accommodates any study design and allows the unmeasured confounder to be discrete or normally distributed we describe applications on two major medical studies

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

stratification and duality for homotopical groups abstract we generalize quillen s f isomorphism theorem quillen s stratification theorem the stable transfer and the finite generation of cohomology rings from finite groups to homotopical groups as a consequence we show that the category of module spectra over c b g f p is stratified and costratified for a large class of p local compact groups g including compact lie groups connected p compact groups and p local finite groups thereby giving a support theoretic classification of all localizing and colocalizing subcategories of this category moreover we prove that p compact groups admit a homotopical form of gorenstein duality

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

solving nonlinear principal agent problems using bilevel programming abstract while significant progress has been made analytic research on principal agent problems that seek closed form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem the principal must maximize expected utility subject to the agent s participation and incentive compatibility constraints linearity of performance measures is often assumed and the linear exponential normal len model is often used to deal with this complexity these assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent in this paper we show how to numerically solve principal agent problems with nonlinear contracts in our procedure we deal directly with the agent s incentive compatibility constraint we illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a len model we also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts a principal agent problem is a special instance of a bilevel nonlinear programming problem we show how to solve principal agent problems by solving bilevel programming problems using the ellipsoid algorithm the approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort

fixed width sequential stopping rules for a class of stochastic programs monte carlo sampling based methods are frequently used in stochastic programming when exact solution is not possible a critical component of monte carlo sampling based methods is determining when to stop sampling to ensure the desired quality of the solutions in this paper we develop stopping rules for sequential sampling procedures that depend on the width of an optimality gap confidence interval estimator the procedures solve a sequence of sampling approximations with increasing sample size to generate solutions and stop when the width of the confidence interval on the current solution s optimality gap plus an inflation factor fall below a prespecified value epsilon we first present a method that takes the schedule of sample sizes as an input and provide guidelines on the growth of sample sizes then we present a method that increases the sample sizes according to the current estimates of the optimality gap the larger the estimates the larger the increases in sample sizes we provide conditi

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

injective dg modules over non positive dg rings abstract let a be an associative non positive differential graded ring in this paper we make a detailed study of a category inj a of left dg modules over a which generalizes the category of injective modules over a ring we give many characterizations of this category generalizing the theory of injective modules and prove a derived version of the bass papp theorem the category inj a is closed in the derived category d a under arbitrary direct sums if and only if the ring h 0 a is left noetherian and for every i 0 the left h 0 a module h i a is finitely generated specializing further to the case of commutative noetherian dg rings we generalize the matlis structure theory of injectives to this context as an application we obtain a concrete version of grothendieck s local duality theorem over commutative noetherian local dg rings

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

stable homotopy groups of spheres we discuss the current state of knowledge of stable homotopy groups of spheres we describe a computational method using motivic homotopy theory viewed as a deformation of classical homotopy theory this yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90 as an application we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90 except for dimension 4 the method relies more heavily on machine computations than previous methods and is therefore less prone to error the main mathematical tool is the adams spectral sequence

nilpotence and descent in equivariant stable homotopy theory abstract let g be a finite group and let f be a family of subgroups of g we introduce a class of g equivariant spectra that we call f nilpotent this definition fits into the general theory of torsion complete and nilpotent objects in a symmetric monoidal stable category with which we begin we then develop some of the basic properties of f nilpotent g spectra which are explored further in the sequel to this paper in the rest of the paper we prove several general structure theorems for categories of module spectra over objects such as equivariant real and complex k theory and borel equivariant mu using these structure theorems and a technique with the flag variety dating back to quillen we then show that large classes of equivariant cohomology theories for which a type of complex orientability holds are nilpotent for the family of abelian subgroups in particular we prove that equivariant real and complex k theory as well as the borel equivariant versions of complex oriented theories have this property

theoremes de dualite pour les corps de fonctions sur des corps locaux superieurs let k be the function field of a smooth projective curve x over a higher dimensional local field k we define tate shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of k coming from a closed point of x we establish duality theorems between tate shafarevich groups for finite groups schemes and for tori

a cohomological classification of vector bundles on smooth affine threefolds we give a cohomological classification of vector bundles of rank 2 on a smooth affine threefold over an algebraically closed field having characteristic unequal to 2 as a consequence we deduce that cancellation holds for rank 2 vector bundles on such varieties the proofs of these results involve three main ingredients first we give a description of the first nonstable a1 homotopy sheaf of the symplectic group second these computations can be used in concert with f morel s a1 homotopy classification of vector bundles on smooth affine schemes and obstruction theoretic techniques stemming from a version of the postnikov tower in a1 homotopy theory to reduce the classification results to cohomology vanishing statements third we prove the required vanishing statements

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

duality in algebra and topology abstract we apply ideas from commutative algebra and morita theory to algebraic topology using ring spectra this allows us to prove new duality results in algebra and topology and to view 1 poincare duality for manifolds 2 gorenstein duality for commutative rings 3 benson carlson duality for cohomology rings of finite groups 4 poincare duality for groups and 5 gross hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon

rost nilpotence and etale motivic cohomology abstract a smooth projective scheme x over a field k is said to satisfy the rost nilpotence principle if any endomorphism of x in the category of chow motives that vanishes on an extension of the base field k is nilpotent we show that an etale motivic analogue of the rost nilpotence principle holds for all smooth projective schemes over a perfect field this provides a new approach to the question of rost nilpotence and allows us to obtain an elegant proof of rost nilpotence for surfaces as well as for birationally ruled threefolds over a field of characteristic 0

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

construction of unipotent galois extensions and massey products abstract for all primes p and for all fields we find a sufficient and necessary condition of the existence of a unipotent galois extension of degree p 6 the main goal of this paper is to describe an explicit construction of such a galois extension over fields admitting such a galois extension this construction is surprising in its simplicity and generality the problem of finding such a construction has been left open since 2003 recently a possible solution of this problem gained urgency because of an effort to extend new advances in galois theory and its relations with massey products in galois cohomology

monoidality of franke s exotic model abstract we discuss the monoidal structure on franke s algebraic model for the k p local stable homotopy category at odd primes and show that its picard group is isomorphic to the integers

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

on the u invariant of function fields of curves over complete discretely valued fields abstract let k be a complete discretely valued field with residue field if char k 0 char 2 and 2 d we prove that there exists an integer n depending on d such that the u invariant of any function field in one variable over k is bounded by n the method of proof is via introducing the notion of uniform boundedness for the p torsion of the brauer group of a field and relating the uniform boundedness of the 2 torsion of the brauer group to the finiteness of the u invariant we prove that the 2 torsion of the brauer group of function fields in one variable over k is uniformly bounded

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

complete modules and torsion modules suppose that r is a ring and that a is a chain complex over r inside the derived category of differential graded a modules there are naturally defined subcategories of a torsion objects and of a complete objects under a finiteness condition on a we develop a morita theory for these subcat egories find conceptual interpretations for some associated algebraic functors and in appropriate commutative situations identify the associated functors as local homology or local cohomology some of the results are suprising even in the case r z and a z p 1 introduction let r be a ring and r mod the derived category of chain complexes of left modules see section 1 2 we choose a fixed complex a which is perfect in other words isomorphic in mod to a complex of finite length in which the entries are finitely generated projective modules we de clare another complex n to be a trivial if hom a a0 0 where hom denotes the chain complex of morphisms in r mod going further we say that x is a torsion if hom x at 0 for all a trivial n9 and that x is a complete if homr n9x 0 for all a trivial n we then study the category ators of a torsion complexes and the category acomp of a complete complexes both of these are triangulated full subcategories of r mod it turns out that these categories are equivalent to one another and also equivalent to the derived category of dif ferential graded modules over the endomorphism complex of a we construct approximation functors celu r mod at0rs and a r mod acomp for an object m of r mod9 the complex celu m is a kind of a cellular approxi mation to m in the sense that it is the best approximation to m which can be cobbled together from a and its suspensions the complex ma is the bousfield localization of m with respect to a homology theory on r mod derived from a we provide algebraic formulas for the functors and find that the functors are related in interesting ways one of which involves an arithmetic square we also show that if cciia r has certain finite dimensionality properties then an object m of r mod is a torsion or a complete if and only if the homology groups 77 m individually satisfy appropriate torsion or completeness conditions suppose now that r is a commutative ring that 7 c r is a finitely generated ideal that a r i9 and that k is the associated koszul complex the complex a

on the behaviour of brauer p dimensions under finitely generated field extensions abstract the present paper shows that if q p or q 0 where p is the set of prime numbers then there exist characteristic q fields e q k k n of brauer dimension brd e q k k and infinite absolute brauer p dimensions abrd p e q k for all p p not dividing q 2 q this ensures that brd p f q k p q 2 q for every finitely generated transcendental extension f q k e q k we also prove that each sequence a p b p p p satisfying the conditions a 2 b 2 and 0 b p a p equals the sequence abrd p e brd p e p p for a field e of characteristic zero

local cohomology of bp_ bp comodules given a spectrum x we construct a spectral sequence of bp bp comodules that converges to bp l n x where l n x is the bousfield localization of x with respect to the johnson wilson theory e n the e 2 term of this spectral sequence consists of the derived functors of an algebraic version of l n we show how to calculate these derived functors which are closely related to local cohomology of bp modules with respect to the ideal i n 1

formulating tightest bounds on causal effects in studies with unmeasured confounders this paper considers the problem of evaluating the causal effect of an exposure on an outcome in observational studies with both measured and unmeasured confounders between the exposure and the outcome under such a situation maclehose et al epidemiology 2005 16 548 555 applied linear programming optimization software to find the minimum and maximum possible values of the causal effect for specific numerical data in this paper we apply the symbolic balke pearl linear programming method probabilistic counterfactuals semantics computation and applications ph d thesis ucla cognitive systems laboratory 1995 j amer statist assoc 1997 92 1172 1176 to derive the simple closed form expressions for the lower and upper bounds on causal effects under various assumptions of monotonicity these universal bounds enable epidemiologists and medical researchers to assess causal effects from observed data with minimum computational effort and they further shed light on the accuracy of the assessment

koszulity of cohomology k π 1 ness quasi formality abstract this paper is a greatly expanded version of 37 section 9 11 a series of definitions and results illustrating the thesis in the title where quasi formality means vanishing of a certain kind of massey multiplications in the cohomology is presented in particular we include a categorical interpretation of the koszulity implies k 1 claim discuss the differences between two versions of massey operations and apply the derived nonhomogeneous koszul duality theory in order to deduce the main theorem in the end we demonstrate a counterexample providing a negative answer to a question of hopkins and wickelgren about formality of the cochain dg algebras of absolute galois groups thus showing that quasi formality cannot be strengthened to formality in the title assertion

assessing solution quality in stochastic programs determining whether a solution is of high quality optimal or near optimal is fundamental in optimization theory and algorithms in this paper we develop monte carlo sampling based procedures for assessing solution quality in stochastic programs quality is defined via the optimality gap and our procedures output is a confidence interval on this gap we review a multiple replications procedure that requires solution of say 30 optimization problems and then we present a result that justifies a computationally simplified single replication procedure that only requires solving one optimization problem even though the single replication procedure is computationally significantly less demanding the resulting confidence interval might have low coverage probability for small sample sizes for some problems we provide variants of this procedure that require two replications instead of one and that perform better empirically we present computational results for a newsvendor problem and for two stage stochastic linear programs from the literature we also discuss when the procedures perform well and when they fail and we propose using optimal solutions to strengthen the performance of our procedures

algebraic morava k theories for any prime q and positive integer t we construct a spectrum k t in the stable homotopy category of schemes over a field k equipped with an embedding k in classical homotopy theory the realization of k t is known as morava k theory the algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic eilenberg maclane spectra which are known to represent motivic cohomology in the stable homotopy category of schemes

local duality in algebra and topology abstract the first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts for any stable category c together with a collection of compact objects k c we construct local cohomology and local homology functors satisfying an abstract version of local duality when specialized to the derived category of a commutative ring a and a suitable ideal in a we recover the classical local duality due to grothendieck as well as generalizations by greenlees and may more generally applying our result to the derived category of quasi coherent sheaves on a quasi compact and separated scheme x implies the local duality theorem of alonso tarrio jeremias lopez and lipman as a second objective we establish local duality for quasi coherent sheaves over many algebraic stacks in particular those arising naturally in stable homotopy theory after constructing an appropriate model of the derived category in terms of comodules over a hopf algebroid we show that in familiar cases the resulting local cohomology and local homology theories coincide with functors previously studied by hovey and strickland furthermore our framework applies to global and local stable homotopy theory in a way which is compatible with the algebraic avatars of these theories in order to aid computability we provide spectral sequences relating the algebraic and topological local duality contexts

k theory and the bridge from motives to noncommutative motives abstract in this work we present a new approach to the theory of noncommutative motives and use it to explain the different flavors of algebraic k theory of schemes and dg categories the work is divided into three main parts in the first part we use the techniques of higher algebra developed in 63 to provide a universal characterization for the symmetric monoidal 1 category underlying the motivic stable a 1 homotopy theory of morel voevodsky 107 67 more precisely given a symmetric monoidal model category v together with an object x v we characterize the underlying symmetric monoidal 1 category of the symmetric monoidal model category sp v x introduced by hovey in 43 by means of a universal property amongst symmetric monoidal 1 categories this characterization trivializes the problem of finding motivic monoidal realizations in the second part we introduce a new approach to the theory of noncommutative motives by constructing a stable motivic homotopy theory for the noncommutative spaces of kontsevich 56 55 54 the key ingredient is a notion of nisnevich topology in the noncommutative setting compatible with the classical notion this compatibility together with the universal property proved in the first part ensures the existence of a canonical monoidal map from the stable motivic theory of morel voevodsky towards these new noncommutative motives that allow us to compare the two theories in the last part of this paper we explain how this bridge can be used to explain the various flavors of algebraic k theory of dg categories more precisely we prove that the non connective k theory of dg categories introduced by schlichting 82 is the non commutative nisnevich sheafification of connective algebraic k theory then we prove that its further non commutative a 1 localization is a tensor unit in our noncommutative motives as a corollary we obtain a precise proof for an original conjecture of kontsevich claiming that k theory gives the correct mapping spaces in noncommutative motives our major application is the discovery of a canonical factorization of our motivic bridge through the 1 category of modules over the commutative algebra object representing homotopy invariant algebraic k theory of schemes the results in 77 imply that this bridge is fully faithful over a field k with resolutions of singularities so that at the motivic level no information below k theory is lost by passing to the noncommutative world

causal conclusions are most sensitive to unobserved binary covariates there is a rich literature that considers whether an observed relation between treatment and response is due to an unobserved covariate in order to quantify this unmeasured bias an assumption is made about the distribution of this unobserved covariate typically that it is either binary or at least confined to the unit interval in this paper this assumption is relaxed in the context of matched pairs with binary treatment and response one might think that a long tailed unobserved covariate could do more damage remarkably that is not the case the most harm is done by a binary covariate so the case commonly considered in the literature is most conservative this has two practical consequences i it is always safe to assume that an unobserved covariate is binary if one is content to make a conservative statement ii when another assumption seems more appropriate say normal covariate there will be less sensitivity than with a binary covariate this assumption implies that it is possible that a relation between treatment and response that is sensitive to unmeasured bias if the unobserved covariate is dichotomous ceases to be sensitive if the unobserved covariate is normally distributed these ideas are illustrated by three examples it is important to note that the claim in this paper applies to our specific setting of matched pairs with binary treatment and response whether the same conclusion holds in other settings is an open question

sensitivity analysis distributional assumptions and confounding assumptions in a presentation of various methods for assessing the sensitivity of regression results to unmeasured confounding lin psaty and kronmal 1998 biometrics54 948 963 use a conditional independence assumption to derive algebraic relationships between the true exposure effect and the apparent exposure effect in a reduced model that does not control for the unmeasured confounding variable however hernan and robins 1999 biometrics55 1316 1317 have noted that if the measured covariates and the unmeasured confounder both affect the exposure of interest then the principal conditional independence assumption that is used to derive these algebraic relationships cannot hold one particular result of lin et al does not rely on the conditional independence assumption but only on assumptions concerning additivity it can be shown that this assumption is satisfied for an entire family of distributions even if both the measured covariates and the unmeasured confounder affect the exposure of interest these considerations clarify the appropriate contexts in which relevant sensitivity analysis techniques can be applied

bounds on potential risks and causal risk differences under assumptions about confounding parameters nonparametric bounds on causal effects in observational studies are available under deterministic potential outcome models we derive narrower bounds by adding assumptions regarding bias due to confounding this bias is defined as the difference between the expectation of potential outcomes for the exposed group and that for the unexposed group we show that crude effect measures bound causal effects under the given assumptions we then derive bounds for randomized studies with noncompliance which are given by the per protocol effect with perfect compliance in one treatment group the direction of effect becomes identifiable under our assumptions although the assumptions are not themselves identifiable they are nonetheless reasonable in some situations

the derived category of quasi coherent sheaves and axiomatic stable homotopy we prove in this paper that for a quasi compact and semi separated nonnecessarily noetherian scheme x the derived category of quasi coherent sheaves over x is a stable homotopy category in the sense of hovey palmieri and strickland answering a question posed by strickland moreover we show that it is unital and algebraic we also prove that for a noetherian semi separated formal scheme its derived category of sheaves of modules with quasi coherent torsion homologies is a stable homotopy category it is algebraic but if the formal scheme is not a usual scheme it is not unital therefore its abstract nature differs essentially from that of the derived category which is equivalent to in the case of a usual scheme

the stack of formal groups in stable homotopy theory we construct the algebraic stack of formal groups and use it to provide a new perspective onto a recent result of m hovey and n strickland on comodule categories for landweber exact algebras this leads to a geometric understanding of their results as well as to a generalisation

a comparison of bayesian and monte carlo sensitivity analysis for unmeasured confounding bias from unmeasured confounding is a persistent concern in observational studies and sensitivity analysis has been proposed as a solution in the recent years probabilistic sensitivity analysis using either monte carlo sensitivity analysis mcsa or bayesian sensitivity analysis bsa has emerged as a practical analytic strategy when there are multiple bias parameters inputs bsa uses bayes theorem to formally combine evidence from the prior distribution and the data in contrast mcsa samples bias parameters directly from the prior distribution intuitively one would think that bsa and mcsa ought to give similar results both methods use similar models and the same prior probability distributions for the bias parameters in this paper we illustrate the surprising finding that bsa and mcsa can give very different results specifically we demonstrate that mcsa can give inaccurate uncertainty assessments e g 95 intervals that do not reflect the data s influence on uncertainty about unmeasured confounding using a data example from epidemiology and simulation studies we show that certain combinations of data and prior distributions can result in dramatic prior to posterior changes in uncertainty about the bias parameters this occurs because the application of bayes theorem in a non identifiable model can sometimes rule out certain patterns of unmeasured confounding that are not compatible with the data consequently the mcsa approach may give 95 intervals that are either too wide or too narrow and that do not have 95 frequentist coverage probability based on our findings we recommend that analysts use bsa for probabilistic sensitivity analysis copyright 2017 john wiley sons ltd