resolution of singularities of threefolds in positive characteristic ii abstract together with vincent cossart olivier piltant resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings j algebra 320 3 2008 1051 1082 this article gives a complete proof of desingularization of quasiprojective varieties of dimensional 3 on fields which are differentially finite over perfect fields

the integral monodromy of hyperelliptic and trielliptic curves we compute the mathbb z ell and mathbb z ell monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves in particular we provide a proof that the mathbb z ell monodromy of the moduli space of hyperelliptic curves of genus g is the symplectic group rm s p2g mathbb z ell we prove that the mathbb z ell monodromy of the moduli space of trielliptic curves with signature r s is the special unitary group rm su r s mathbb z ell otimes mathbb z zeta 3

complexes de chaines etales et courbes de deligne lusztig abstract in a first part we lift the usual constructions of functors between derived categories of etale sheaves over schemes with a sheaf of algebras to pure derived categories for varieties with finite group actions we recover in a more functorial way rickard s construction we apply this to the case of deligne lusztig varieties and show that broue s conjecture holds for curves the additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

galois embeddings for linear groups a criterion is given for the solvability of a central galois embedding problem to go from a projective linear group covering to a vectorial linear group covering

some 4 point hurwitz numbers in positive characteristic author s bouw irene i osserman brian abstract in this paper we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p our techniques involve related computations in the case of three branch points and allow us to conclude in many cases that for a particular choice of degeneration all the covers we consider degenerate to separable admissible covers starting from a good understanding of the complex case the proof is centered on the theory of stable reduction of galois covers

ramification of valuations abstract in this paper we develop a very explicit theory of ramification of general valuations in algebraic function fields in characteristic zero and arbitrary dimension we obtain the strongest possible generalization of the classical ramification theory of local dedekind domains we further develop a ramification theory of algebraic functions fields of dimension two in positive characteristic we prove that local monomialization and simultaneous resolution hold under very mild assumptions and give pathological examples

local systems and finite unitary and symplectic groups abstract for powers q of any odd prime p and any integer n 2 we exhibit explicit local systems on the affine line a 1 in characteristic p 0 if 2 n and on the affine plane a 2 if 2 n whose geometric monodromy groups are the finite symplectic groups sp 2 n q when n 3 is odd we show that the explicit rigid local systems on the affine line in characteristic p 0 constructed in 11 do have the special unitary groups su n q as their geometric monodromy groups as conjectured therein and also prove another conjecture of 11 that predicted their arithmetic monodromy groups

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

dynamic behaviors of the impulsive periodic multi species predator prey system the dynamic behaviors of an impulsive periodic predator prey model with n preys and m predators are studied in this paper by constructing a suitable lyapunov function and using the comparison theorem of impulsive differential equation sufficient conditions which ensure the permanence and global attractivity of the system are obtained at the same time a set of criteria which guarantee that some species in the system are permanent and globally attractive while the remaining species are driven to extinction is obtained our results show that for the multi species predator prey community impulsivity is one of the important reasons that can change the long time behaviors of species

split embedding problems over complete domains we prove that every finite split embedding problem is solvable over the field k x1 x n of formal power series in n 2 variables over an arbitrary field k as well as over the field quot a x 1 x n of formal power series in n 1 variables over a noetherian integrally closed domain a this generalizes a theorem of harbater and stevenson who settled the case k x1 x 2

the fundamental group of affine curves in positive characteristic abstract it is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over an uncountable algebraically closed field k of positive characteristic is a profinite free group of rank equal to the cardinality of k

a class of exceptional polynomials we present a class of indecomposable polynomials of non primepower degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field the associated geometric monodromy groups are the simple groups where k 3 and odd the first member of this class was previously found by p muller 17 this realises one of only two possibilities for such a class which remain following deep work of fried guralnick and saxl 7 the other is associated with psl 3 k 3 and odd in fields of characteristic 3

stable generalized predictive control with constraints and bounded disturbances disturbances in the presence of constraints can drive predictive control into infeasibility and instability this problem has attracted little research effort despite its significant practical importance earlier work has given stability conditions but these are restricted to systems with at most one unstable pole and do not lead to suitable algorithms because they apply to infinite horizons only here we modify the constraint limits and derive an algorithm with guaranteed stability and asymptotic tracking available degrees of freedom are given up in order to optimize performance the results of the paper are illustrated by means of numerical examples

on colmez s product formula for periods of cm abelian varieties colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field k analogous to the standard product formula in algebraic number theory he proved this conjecture up to a rational power of 2 for k mathbb q abelian in this paper we complete the proof of colmez for k mathbb q abelian by eliminating this power of 2 our proof relies on analyzing the galois action on the de rham cohomology of fermat curves in mixed characteristic 0 2 which in turn relies on understanding the stable reduction of mathbb z 2 n covers of the projective line branched at three points

asymptotic stability of competitive systems with delays and impulsive perturbations abstract a general impulsive nonautonomous lotka volterra system of integro differential equations with infinite delay is considered the impulses are realized at fixed moments of time sufficient conditions for uniform stability and asymptotic stability of solutions are investigated the main results are obtained by using the comparison principle and the lyapunov method

global attractivity of an almost periodic n species nonlinear ecological competitive model abstract by using comparison theorem and constructing suitable lyapunov functional we study the following almost periodic nonlinear n species competitive lotka volterra model x i t x i t r i t j 1 n a i j t x j i j t j 1 n b i j t x j i j t i j t j 1 n c i j t x i i i t x j i j t a set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model as applications some special competition models are studied again our new results improve and generalize former results examples and their simulations show the feasibility of our main results

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

polynomials with psl 2 monodromy let k be a field of characteristic p 0 let q be a power of p and let u be transcendental over k we determine all polynomials f k x k x p of degree q q 1 2 for which the galois group of f x u over k u has a transitive normal subgroup isomorphic to psl 2 q subject to a certain ramification hypothesis as a consequence we describe all polynomials f k x such that deg f is not a power of p and f is functionally indecomposable over k but f decomposes over an extension of k moreover except for one ramification configuration which is handled in a companion paper with rosenberg we describe all indecomposable polynomials f k x such that deg f is not a power of p and f is exceptional in the sense that x y is the only absolutely irreducible factor of f x f y which lies in k x y it is known that when k is finite a polynomial f is exceptional if and only if it induces a bijection on infinitely many finite extensions of k

embedding problems over large fields in this paper we study galois theoretic properties of a large class of fields a class which includes all fields satisfying a universal local global principle for the existence of rational points on varieties as applications we give a positive answer to a long standing conjecture which originates in an unpublished note of roquette and asserts that the absolute galois group of a countable hilbertian pac field is profinite free see f j problem 24 41 secondly we give new evidence for the conjecture of shafarevich which asserts that the absolute galois group of qab is profinite free finally one of the most interesting applications of the theory we develop here is the insight in the galois structure of the totally eg adic numbers

cyclic quotients of transitive groups abstract let a be a transitive subgroup of s n we show that the largest cyclic quotient of a has order at most n this can be interpreted as an equivalent result about extensions of constants in the galois closure of a covering of curves over a finite field we also prove that the point stabilizer in a finite primitive permutation group always has a faithful orbit

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

patching and thickening problems in recent years much progress has been made on the structure of fundamental groups of algebraic curves by means of patching techniques in formal and rigid geometry a number of these results have concerned curves over algebraically closed fields of characteristic p e g the proofs of the abhyankar conjecture ra ha5 and of the geometric case of the shafarevich conjecture po1 ha6 and the realization of galois groups over projective curves sa1 st1 while the rigid approach to patching is often regarded as more intuitive than the formal approach its foundations are less well established but constructions involving the formal approach have tended to be technically more cumbersome the purpose of the current paper is to build on previous formal patching results in order to create a framework in which such constructions are facilitated in the process we prove a result asserting that singular curves over a field k can be thickened to curves over k t with prescribed behavior in a formal neighborhood of the singular locus and similarly for covers of curves afterwards we obtain applications to fundamental groups of curves over large fields the structure of the paper is as follows section 1 concerns patching problems for projective curves x over a power series ring r k t1 tn it is shown theorem 1 that giving a coherent projective module over x is equivalent to giving such modules compatibly on a formal neighborhood of each singular point of the closed fibre x and on the formal thickening along the complement of the singular locus s of x section 2 applies this to thickening problems in both the absolute and relative senses namely it shows theorem 3 that such an x can be constructed from its closed fibre x and from complete local thickenings near s such that x is a trivial deformation away from s moreover theorem 2 given a morphism x z and a thickening z of z such that the local thickenings near s are compatible with that of z there is a unique such thickening x of x that is compatible with the given data in section 3 these results are applied to the problem of thickening and deforming covers theorem 4 there combines the results of sections 1 and 2 to show that covers of reducible k curves can be thickened to covers of curves over k t and theorem 5 then shows how this can be used over large fields to

tchebotarev theorems for function fields abstract the central theme of the paper is the specialization of algebraic function field extensions our main results are tchebotarev type theorems for galois function field extensions finite or infinite over various base fields under some conditions we extend the classical finite field case to number fields p adic fields pac fields function fields x etc we also compare the tchebotarev conclusion existence of unramified local specializations with galois group any cyclic subgroup of the generic galois group up to conjugation to the hilbert specialization property for a function field extension with the tchebotarev property the exponent of the galois group is bounded by the l c m of the local specialization degrees local global questions arise for which we provide answers examples and counter examples

families of wildly ramified covers of curves in this paper i investigate wildly ramified g galois covers of curves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i branched at exactly one point over an algebraically closed field k of characteristic p i answer a question of m raynaud by showing that proper families of such covers of a twisted projective line are isotrivial the method is to construct an affine moduli space for covers whose inertia group is of the form inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i there are two other applications of this space in the case that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i the first uses formal patching to compute the dimension of the space of nonisotrivial deformations of in terms of the lower jump of the filtration of higher inertia groups the second gives necessary criteria for good reduction of families of such covers these results will be used in a future paper to prove the existence of such covers with specified ramification data

on hilbertian ideals abhyankar defined the index of a monomial in a matrix of indeterminates x to be the maximal size of any minor of x whose principal diagonal divides the given monomial using this concept he characterized a free basis for general type of determinantal ideals formed by the minors coming from a saturated subset of x in this paper to a monomial in x of index p we associate a combinatorial object called a superskeleton of latitude p which can loosely be described as a p tuple of almost nonintersecting paths in a rectangular lattice of points using this map we prove that the ideal generated by the p by p minors of a saturated set in x is hilbertian i e the hilbert polynomial of this ideal coincides with its hilbert function for all nonnegative integers

wild ramification and a vanishing cycles formula in duke math j 55 1987 629 659 k kato proved using techniques from k theory a formula which compares the dimensions of the spaces of vanishing cycles in a finite morphism between formal germs of curves over a complete discrete valuation ring to the best of my knowledge kato s formula is explicit only in the case where this morphism is generically separable on the level of special fibres in this note we prove using formal patching techniques a la harbater an analogous explicit formula in the case of a galois cover of degree p between formal germs of curves over a complete discrete valuation ring of unequal characteristic 0 p which includes the case where we have inseparability on the level of special fibres the results of this paper play a key role in math ag 0106249 where is studied the semi stable reduction of galois covers of degree p of curves over a complete discrete valuation ring of unequal characteristics 0 p as well as the galois action on these covers

galois groups of unramified covers of projective curves in characteristicp abstract we show several results concerning the finite groups that occur as galois groups of unramified covers of projective curves in characteristic p in particular we prove that every finite group with g generators occurs over some curve of genus g this implies for example that every finite simple group occurs in genus 2 by similar methods we obtain several other families of groups which occur in genus 2 in addition we show that if a group g occurs over some curve of genus g then it must occur over almost all curves of genus g or greater the results are obtained using formal patching

computationally efficient algorithms for constraint handling with guaranteed stability and near optimality predictive control strategies allow for the systematic handling of constraint performance and stability however the associated algorithms can be computational burdensome and or difficult to unravel the aim of this paper is to discuss and compare algorithms based on invariant sets which meet the additional requirement for computational simplicity there may of course be a concomitant loss of optimality but as illustrated this can be minimal and often is a small price to pay when one considers the significant improvements in efficiency

bivariate factorizations connecting dickson polynomials and galois theory in his ph d thesis of 1897 dickson introduced certain permutation polynomials whose galois groups are essentially the dihedral groups these are now called dickson polynomials of the first kind to distinguish them from their variations introduced by schur in 1923 which are now called dickson polynomials of the second kind in the last few decades there have been extensive investigations of both of these types which are related to the classical chebyshev polynomials we give new bivariate factorizations involving both types of dickson polynomials these factorizations demonstrate certain isomorphisms between dihedral groups and orthogonal groups and lead to the construction of explicit equations with orthogonal groups as galois groups

rigidity reduction and ramification in this paper we consider wildly ramified g galois covers of curves f y 1k branched at exactly one point over an algebraically closed field k of characteristic p for g equal to ap or psl2 p we prove abhyankar s inertia conjecture that all possible inertia groups occur over infinity for such covers f in addition we prove that the set of conductors that can be realized depends on the group the method we use is to compute the reduction of galois covers of mathbb p 1 overline mathbb q branched at 3 points we observe that the existence of covers with given inertia in characteristic p is closely related to the arithmetic of covers in characteristic zero

brief an efficient off line formulation of robust model predictive control using linear matrix inequalities the practicality of model predictive control mpc is partially limited by its ability to solve optimization problems in real time moreover on line computational demand for synthesizing a robust mpc algorithm will likely grow significantly with the problem size in this paper we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained mpc algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off line one within another in state space this off line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed loop system and substantial reduction of the on line mpc computation the controller design is illustrated with two examples

further nice equations for nice groups nice sextinomial equations are given for unramified coverings of the affine line in nonzero characteristic p with p 2m q and 2m q as galois groups where m 3 is any integer and q 1 is any power of p 2

deformations formelles des revetements sauvagement ramifies de courbes algebriques in this paper we study formal moduli for wildly ramified galois covering we prove a local global principle we then focus on the infinitesimal deformations of the z pz covers we explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p 2 by deforming artin schreier equations we obtain a lower bound on the dimension of the local versal deformation ring at last by comparing the global versal deformation ring to the complete local ring in a point of a moduli space we determine the dimensions of the global and local versal deformation rings

global exponential stability for impulsive cellular neural networks with time varying delays abstract in this paper we study the problem of global exponential stability for cellular neural networks cnn with time varying delays and fixed moments of impulsive effect we establish several stability criteria by employing lyapunov functions and the razumikhin technique

systems with persistent disturbances predictive control with restricted constraints predictive regulation of linear discrete time systems subject to unknown but bounded disturbances and to state control constraints is addressed an algorithm based on constraint restrictions is presented and its stability properties are analysed

global attractivity of the almost periodic solution of a delay logistic population model with impulses in this paper we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations by using a comparison theorem and constructing a suitable lyapunov functional a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained as applications some special models are studied our new results improve and generalize former results

torsors under finite and flat group schemes of rank p with galois action in this note we study the geometry of torsors under flat and finite commutative group schemes of rank p above curves in characteristic p and above relative curves over a complete discrete valuation ring of inequal characteristic in both cases we study the galois action of the galois group of the base field on these torsors we also study the degeneration of p torsors from characteritic 0 to characteristic p and show that this degeneration is compatible with the galois action we then discuss the lifting of torsors under flat and commutative group schemes of rank p from positive to zero characteristics finally for a proper and smooth curve x over a complete discrete valuation field of inequal characteristic which has good reduction we show the existence of a canonical galois equivariant filtration on the first etale cohomology group of the geometric fibre of x with values in p

effective methods for vanishing cycles of p cyclic covers of the p adic line abstract this paper studies the stable reduction of p cyclic covers x p k 1 of the projective line over p adic fields so far an algorithm to effectively determine the stable reduction of such covers is only known under additional hypothesis on the branch locus of the cover here rather than restricting the type of cover we consider the general case and obtain results on the structure of the special fiber xk of the stable reduction of x special attention is payed to making all constructions effective the central result is a formula computing the number of vanishing cycles on xk in particular we give criteria for the special fiber of the stable reduction to be tree like and for when x is a mumford curve refining the analysis of vanishing cycles we describe an algorithm that computes all the components of positive p rank in the stable model

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

robust stability in constrained predictive control through the youla parameterisations in this article we take advantage of the primary and dual youla parameterisations to set up a soft constrained model predictive control mpc scheme in this framework it is possible to guarantee stability in face of norm bounded uncertainties under special conditions guarantees are also given for hard input constraints in more detail we parameterise the mpc predictions in terms of the primary youla parameter and use this parameter as the on line optimisation variable the uncertainty is parameterised in terms of the dual youla parameter stability can then be guaranteed through small gain arguments on the loop consisting of the primary and dual youla parameter this is included in the mpc optimisation as a constraint on the induced gain of the optimisation variable we illustrate the method with a numerical simulation example

formal and rigid geometry in 1974 raynaud proposed a program raynaud in mem soc math fr 39 40 319 327 1974 where he introduced groundbreaking ideas to rigid geometry by interpreting a rigid analytic space as the generic fiber of a formal schemes over operatorname spf r here operatorname spf r is always the formal spectrum of a complete valuation ring r of height 1 where its topology is given by an ideal pi for some element pi in r with 0 pi 1 due to results on flat modules raynaud and gruson in invent math 13 1 89 1971 his approach also works in the non noetherian case of formal schemes of topologically finite presentation over operatorname spf r

normal subgroups of the algebraic fundamental group of affine curves in positive characteristic let 1 c be the algebraic fundamental group of a smooth connected affine curve defined over an algebraically closed field of characteristic p 0 of countable cardinality let n be a normal respectively characteristic subgroup of 1 c under the hypothesis that the quotient 1 c n admits an infinitely generated sylow p subgroup we prove that n is indeed isomorphic to a normal respectively characteristic subgroup of a free profinite group of countable cardinality as a consequence every proper open subgroup of n is a free profinite group of countable cardinality

fundamental group in positive characteristic abstract it is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic is profinite free of countable rank a description of the abelianizations of the fundamental groups of affine curves over an algebraically closed field of nonzero characteristic is also given

resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings abstract in dimension 3 the desingularization problem is reduced to local uniformization on artin schreier and purely inseparable coverings of regular space

the oort conjecture on lifting covers of curves we show that the conjecture of oort on lifting covers of curves is true the main ingredients in the proof are a deformation argument in characteristic p and a special case of a very recent result by obus wewers a kind of boundedness result is given as well