nombres de weil sommes de gauss et annulateurs galoisiens for an abelian number field k containing a primitive p rm th root of unity p an odd prime and satisfying certain technical conditions we parametrize the bbb z p rm g k bbb q annihilators of the minus part a k of the p class group by means of modules of jacobi sums using a reflection theorem and bloch kato s reciprocity law we then determine the fitting ideal of the plus part a k in terms of twisted gauss sums

galois representations mumford tate groups and good reduction of abelian varieties let k be a number field and a an abelian variety over k we are interested in the following conjecture of morita if the mumford tate group of a does not contain unipotent rational points then a has potentially good reduction at any discrete place of k the mumford tate group is an object of analytical nature whereas having good reduction is an arithmetical notion linked to the ramification of galois representations this conjecture has been proved by morita for particular abelian varieties with many endomorphisms called of pel type noot obtained results for abelian varieties without nontrivial endomorphisms mumford s example not of pel type we give new results for abelian varieties not of pel type

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

a p adic regulator problem in algebraic k theory and group cohomology is injective where p is a fixed rational prime and n 1 is odd observe that each p is clearly injective for n 1 because ki 0 0 and k op op a much harder problem is whether zp is injective for n 1 and f totally real abelian injectively of zp on the subgroup of 0 consisting of those elements congruent to lmodp for each p p is equivalent to nonvanishing of the p adic regulator br c as an example of 1 let f be quadratic imaginary then is

a non abelian conjecture of tate shafarevich type for hyperbolic curves let x denote a hyperbolic curve over mathbb q and let p denote a prime of good reduction the third author s approach to integral points introduced in kim invent math 161 629 656 2005 publ res inst math sci 45 89 133 2009 endows x mathbb z p with a nested sequence of subsets x mathbb z p n which contain x mathbb z these sets have been computed in a range of special cases balakrishnan et al j am math soc 24 281 291 2011 dan cohen and wewers proc lond math soc 110 133 171 2015 dan cohen and wewers int math res not imrn 17 5291 5354 2016 kim j am math soc 23 725 747 2010 there is good reason to believe them to be practically computable in general in 2012 the third author announced the conjecture that for n sufficiently large x mathbb z x mathbb z p n this conjecture may be seen as a sort of compromise between the abelian confines of the bsd conjecture and the profinite world of the grothendieck section conjecture after stating the conjecture and explaining its relationship to these other conjectures we explore a range of special cases in which the new conjecture can be verified

diagonal cycles and euler systems ii the birch and swinnerton dyer conjecture for hasse weil artin l functions this article establishes new cases of the birch and swinnerton dyer conjecture in analytic rank 0 for elliptic curves over mathbb q viewed over the fields cut out by certain self dual artin representations of dimension at most 4 when the associated l function vanishes to even order ge 2 at its central point two canonical classes in the corresponding selmer group are constructed and shown to be linearly independent assuming the non vanishing of a garrett hida p adic l function at a point lying outside its range of classical interpolation the key tool for both results is the study of certain p adic families of global galois cohomology classes arising from gross kudla schoen diagonal cycles in a tower of triple products of modular curves

the construction of exact d optimum experimental designs with application to blocking response surface designs summary the properties of optimum designs are investigated when there are both qualitative and quantitative factors algorithms for the construction of exact designs are described which are of general applicability the case when the qualitative factors represent blocking variables is given special treatment a modified algorithm provides the opportunity to divide the experimental trials into blocks of specified sizes examples are given of second order models in the quantitative factors divided into two or three blocks of a variety of sizes use of the adjustment algorithm to improve such designs generated from a list of candidate points is demonstrated

li p service an algorithm for computing p adic polylogarithms we describe an algorithm for computing coleman s p adic poly logarithms up to a given precision 2007 american mathematical society

pseudomonotone and copositive star matrices abstract we study general and complementarity properties of matrices which are either pseudomonotone or copositive star on a closed convex cone in particular we show that if a matrix is pseudomonotone on the nonnegative orthant of r n then it belongs to p 0 q 0 we also show that if a matrix t is copositive star on a closed convex cone k then the linear complementarity problem lcp t k q is solvable for all q in r n iff zero is the only solution of the homogeneous problem lcp t k 0 we characterize pseudomonotonicity of a matrix t by the nonnegativity of the quadratic form tx x on a certain set

torsion points on curves and p adic abelian integrals theorem a let f c j be an albanese morphism defined over a number field k of a s mooth curve of genus g into its jacobian suppose j has potential complex multiplication let s denote the set of primes p of k satisfying i p does not divide 2 or 3 ii k q is unramified at p iii c has good ordinary reduction over k then the set t of torsion points of a defined over an algebraic closure of k which lie on the image of c is defined over an extension of k unramified above s moreover to pg

stability results for polyhedral complementarity problems in this work we study the multivalued complementarity problem for polyhedral multifunctions under homogeneity assumptions we employ an approach that consists in approximating the equivalent variational inequality formulation of the problem and studying the asymptotic behavior of sequences of solutions to these approximation problems to do this we employ results and the language of variational analysis the novelty of this approach lies in the fact that it allows us to obtain not only existence results but also stability ones we consider that our results can be used for developing numerical algorithms for solving multivalued complementarity problems

p adic multiple zeta values ii tannakian interpretations we establish a tannakian formalism of p adic multiple polylogarithms and p adic multiple zeta values introduced in our previous paper via a comparison isomorphism between a de rham fundamental torsor and a rigid fundamental torsor of the projective line minus three points and also discuss its hodge and e tale analogues as an application we give a way to erase log poles of p adic multiple polylogarithms and introduce overconvergent p adic multiple polylogarithms which might be p adic multiple analogue of zagier s single valued complex polylogarithms

the iwasawa conjecture for totally real fields let f be a totally real number field let p be a prime number and for any integer n let fun denote the group of nth roots of unity let 41 be a p adic valued artin character for f and let f be the extension of f attached to 4 i e so that 4 is the character of a faithful representation of gal f f we will assume that f is also totally real for a number field k let k denote the cyclotomic zp extension of k following greenberg we say that 4 is of type s if f n fc f and of type w if 4 is one dimensional with f p c fcc deligne and ribet in dr following kubota and leopoldt for the case f q have proved the existence of a p adic l function associated to a one dimensional artin character 4 with f totally real this function lp s 4 is continuous for s e zp 1 and even at s 1 if 4 is not trivial and satisfies the following interpolation property

the cech filtration and monodromy in log crystalline cohomology for a strictly semistable log scheme y over a perfect field k of characteristic p we investigate the canonical cech spectral sequence c t abutting the hyodo kato log crystalline cohomology h crys y t q of y and beginning with the log convergent cohomology of its various component intersections y i we compare the filtration on h crys y t q arising from c t with the monodromy operator n on h crys y t q we also express n through residue maps and study relations with singular cohomology if y lifts to a proper strictly semistable formal scheme x over a finite totally ramified extension of w k with generic fibre x k we obtain results on how the simplicial structure of x an k as analytic space is reflected in h dr x k h dr x an k

coleman integration using the tannakian formalism we use a new idea to construct a theory of iterated coleman functions on overconvergent spaces with good reduction in any dimension a coleman function in this theory consists of a unipotent differential equation a functional on the underlying bundle and a solution to the equation on a residue class the new idea is to use the theory of tannakian categories and the action of frobenius to analytically continue solutions of the differential equation to all residue classes

spectral theory for p adic operators we establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix for this sake we define the notion of normality of a p adic operator and give several criteria for the normality we study the relation between the normality and the reduction in the finite dimensional case the normality of an operator is equivalent to the diagonalisability of a matrix by a unitary matrix therefore we also study the relation between the diagonalisability and the reduction for example we show that the diagonalisation of the reduction gives a partition of unity corresponding to the reduction of the spectrum which gives a functorial lift of the eigenspace decomposition of the reduction

design of experiments with both mixture and qualitative factors while the remaining l factors are qualitative i e they take only a distinct number of possible values the conditions for optimality of approximate designs for the general case of experiments with qualitative and quantitative factors have been established by kurotschka 1981 1987 and wierich 1986 exact designs for such experiments are described in atkinson and donev 1989 but neither set of researchers gives any special treatment to experiments with mixtures the mixture constraint 1 however introduces some special features which it is the purpose of this paper to investigate in section 2 some useful properties of the mixture experiments are listed in section 3 models and optimality conditions for experiments with mixture and qualitative factors are established discussion with examples is given in section 4 in section 5 more general mixture experiments are considered in which the response depends on the amount of the mixture as well as on the proportions of its components experiments of this kind are common in such areas as chemistry medicine and agriculture

smooth p adic analytic spaces are locally contractible 0 introduction 293 1 piecewise rs linear spaces 298 2 r colored polysimplicial sets 308 3 r colored polysimplicial sets of length l 313 4 the skeleton of a nondegenerate pluri stable formal scheme 327 5 a colored polysimplicial set associated with a nondegenerate poly stable fibration 336 6 p adic analytic and piecewise linear spaces 346 7 strong local contractibility of smooth analytic spaces 355 8 cohomology with coefficients in the sheaf of constant functions 362

stable monotone variational inequalities variational inequalities associated with monotone operators possibly nonlinear and multivalued and convex sets possibly unbounded are studied in reflexive banach spaces a variety of results are given which relate to a stability concept involving a natural parameter these include characterizations useful as criteria for stable existence of solutions and also several characterizations of surjectivity the monotone complementarity problem is covered as a special case and the results are sharpened for linear monotone complementarity and for generalized linear programming

on integrality of p adic iterated integrals abstract the purpose of this paper is to prove integrality for certain p adic iterated coleman integrals as underlying geometry we will take the complement of a divisor d x with good reduction where x is the projective line or an elliptic curve over the witt vectors of a perfect characteristic p field as a corollary we prove a lower bound for the valuations of p adic multiple zeta values

some existence results for multivalued complementarity problems this paper presents some new results for the existence of a solution to a multivalued complementary problem these results are derived under a upper limiting homogeneity ulh property on the multifunction defining the complementarity problem and on a certain closedness interiority condition the closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem we show that this closedness condition is satisfied by the class of polyhedral multifunctions

p adic multiple zeta values i our main aim in this paper is to give a foundation of the theory of p adic multiple zeta values we introduce one variable p adic multiple polylogarithms by coleman s p adic iterated integration theory we define p adic multiple zeta values to be special values of p adic multiple polylogarithms we consider the formal p adic kz equation and introduce the p adic drinfel d associator by using certain two fundamental solutions of the p adic kz equation we show that our p adic multiple polylogarithms appear as coefficients of a certain fundamental solution of the p adic kz equation and our p adic multiple zeta values appear as coefficients of the p adic drinfel d associator we show various properties of p adic multiple zeta values which are sometimes analogous to the complex case and are sometimes peculiar to the p adic case via the p adic kz equation

even more with the lemke complementarity algorithm this note presents a new termination result for the lemke linear complementarity algorithm that unifies two previous results special cases include linear complementarity problems satisfying the evers condition and those whosem matrix is copositive plus

weakly homogeneous variational inequalities and solvability of nonlinear equations over cones given a closed convex cone c in a finite dimensional real hilbert space h a weakly homogeneous map f c rightarrow h is a sum of two continuous maps h and g where h is positively homogeneous of degree gamma ge 0 on c and g x o x gamma as x rightarrow infty in c given such a map f a nonempty closed convex subset k of c and a q in h we consider the variational inequality problem text vi f k q of finding an x in k such that langle f x q x x rangle ge 0 for all x in k in this paper we establish some results connecting the variational inequality problem text vi f k q and the cone complementarity problem text cp f infty k infty 0 where f infty h is the homogeneous part of f and k infty is the recession cone of k we show for example that text vi f k q has a nonempty compact solution set for every q when zero is the only solution of text cp f infty k infty 0 and the topological index of the map x mapsto x pi k infty x g x at the origin is nonzero where g is a continuous extension of f infty to h as a consequence we generalize a complementarity result of karamardian j optim theory appl 19 227 232 1976 formulated for homogeneous maps on proper cones to variational inequalities the results above extend some similar results proved for affine variational inequalities and for polynomial complementarity problems over the nonnegative orthant in mathcal r n as an application we discuss the solvability of nonlinear equations corresponding to weakly homogeneous maps over closed convex cones in particular we extend a result of hillar and johnson proc am math soc 132 945 953 2004 on the solvability of symmetric word equations to euclidean jordan algebras

models for mixture experiments when the response depends on the total amount the usual definition of a mixture experiment requires that the response depend only on the proportions of the mixture components and not on the total amount of the mixture we consider mixture experiments in which the response also depends on the total amount and we develop mixture amount models appropriate for such situations models in the component amounts are also considered and are shown to be reduced forms of the mixture amount models examples are used to illustrate the development interpretation and comparison of the models

a p adic nonabelian criterion for good reduction of curves let k be a complete discrete valuation field of characteristic 0 with valuation ring ok and perfect residue field k of positive characteristic p we prove that a proper and smooth curve over k admitting a semistable model over ok has good reduction if and only if its unipotent p adic etale fundamental group is crystalline

on multivalued complementarity problems in banach spaces in this paper we prove a new existence result for multivalued complementarity problems in banach spaces our result represents a refinement and improvement of the previously known results

darmon points on elliptic curves over number fields of arbitrary signature we present new constructions of complex and pp adic darmon points on elliptic curves over base fields of arbitrary signature we conjecture that these points are global and present numerical evidence to support our conjecture

on p adic invariant cycles theorem for a proper semistable curve x over a dvr of mixed characteristics and perfect residue field we prove the invariant cycles theorem with trivial coefficients i e that the group of elements of the first de rham cohomology group of the generic fiber of x annihilated by the monodromy operator coincides with the first rigid cohomology group of its special fiber this is done using an explicit description of the monodromy operator on the de rham cohomology of the generic fiber of x with coefficients a convergent f isocrystal see 11 and the proof exhibits an interesting interplay between this cohomology group and the com binatorics of the graph of the reduction of x the result was proved in a different way in the case the dvr has finite residue field in 4 we also study the case where the coefficients are unipotent convergent f isocrystals on the special fiber of x without log structure we show that the invariant cycles theorem does not hold in general in this setting and give a sufficient condition for non exactness

good reduction criterion for k3 surfaces we prove a neron ogg shafarevich type criterion for good reduction of k3 surfaces which states that a k3 surface over a complete discrete valuation field has potential good reduction if its l adic cohomology group is unramified we also prove a p adic version of the criterion these are analogues of the criteria for good reduction of abelian varieties the model of the surface will be in general not a scheme but an algebraic space as a corollary of the criterion we obtain the surjectivity of the period map of k3 surfaces in positive characteristic

a class of p adic galois representations arising from abelian varieties over let v be a p adic representation of the absolute galois group g of open image in new window that becomes crystalline over a finite tame extension and assume p 2 we provide necessary and sufficient conditions for v to be isomorphic to the p adic tate module vp open image in new window of an abelian variety open image in new window defined over open image in new window these conditions are stated on the filtered g module attached to v

syntomic regulators and special values of p adic l functions in this paper p adic analogs of the lichtenbaum conjectures are proven for abelian number fields f and odd prime numbers p which generalize leopoldt s p adic class number formula and express special values of p adic l functions in terms of orders of k groups and higher p adic regulators the approach uses syntomic regulator maps which are the p adic equivalent of the beilinson regulator maps they can be compared with etale regulators via the fontaine messing map and computations of bloch kato in the case that p is unramified in f lead to results about generalized coates wiles homomorphisms and cyclotomic characters