vertexwise criteria for admissibility of alcoves we give a new description of the set rm adm mu of admissible alcoves as an intersection of certain obtuse cones of alcoves and we show this description may be given by imposing conditions vertexwise we use this to prove the vertexwise admissibility conjecture of pappas rapoport smithling the same idea gives simple proofs of two ingredients used in the proof of the kottwitz rapoport conjecture on existence of crystals with additional structure

hasse schmidt derivations and coefficient fields in positive characteristics abstract we show how to express any hasse schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis as an application we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of hasse schmidt derivations

truncations of level 1 of elements in the loop group of a reductive group the aim of this article is to dene and study a new invariant of elements of loop groups that is invariant under conjugation by a hyperspecial maximal open subgroup and that we call the truncation of level 1 we classify truncations of level 1 and describe their specialization behavior furthermore we prove group theoretic conditions for the set of conjugacy classes obtained from elements of a given truncation of level 1 and in particular for the generic conjugacy class in any given truncation stratum in the last section we relate our invariant to the ekedahl oort stratication of the siegel moduli space and to generalizations to other pel shimura varieties

minimal p divisible groups a p divisible group x can be seen as a tower of building blocks each of which is isomorphic to the same finite group scheme x p clearly if x1 and x2 are isomorphic then x1 p x2 p however conversely x1 p x2 p does in general not imply that x1 and x2 are isomorphic can we give over an algebraically closed field in characteristic p a condition on the p kernels which ensures this converse here are two known examples of such a condition consider the case that x is ordinary or the case that x is superspecial x is the p divisible group of a product of supersingular elliptic curves in these cases the p kernel uniquely determines x

character sheaves v this paper is part of a series s 131 devoted to the study of a class g of irreducible perverse sheaves called character sheaves on a connected reductive algebraic group g the numbering of chapters sections and references will continue that of s 131 this paper is a step towards the classification of character sheaves on g one of the main results is the following one under certain assumptions there is a natural surjective map with finite fibers from g to the set of all pairs 9 c up to conjugacy by the weyl group where 9 is a tame local system on the maximal torus and c is a two sided cell in the stabilizer w of 9 in the weyl group the assumptions made on g are

dimension formula for the affine deligne lusztig variety x mu b x μ b the study of certain union x mu b of affine deligne lusztig varieties in the affine flag varieties arose from the study of shimura varieties with iwahori level structure in this paper we give an explicit dimension formula for x mu b associated to sufficiently large dominant coweight mu

the newton stratification on deformations of local g shtukas bounded local g shtukas are function field analogs for p divisible groups with extra structure we describe their deformations and moduli spaces the latter are analogous to rapoport zink spaces for p divisible groups the underlying schemes of these moduli spaces are a ne deligne lusztig varieties for basic newton polygons the closed newton stratum in the universal deformation of a local g shtuka is isomorphic to the completion of a corresponding a ne deligne lusztig variety in that point this yields bounds on the dimension and proves equidimensionality of the basic a ne deligne lusztig varieties

minimal length elements in twisted conjugacy classes of finite coxeter groups let w be a finite coxeter group and let f be an automorphism of w that leaves the set of generators of w invariant we establish certain properties of elements of minimal length in the f conjugacy classes of w that allow us to define character tables for the corresponding twisted iwahori hecke algebras these results are extensions of results obtained by geck and pfeiffer in the case where f is trivial

on the μ ordinary locus of a shimura variety abstract in this paper we study the ordinary locus of a shimura variety with parahoric level structure under the axioms in 12 we show that ordinary locus is a union of certain maximal ekedahl kottwitz oort rapoport strata introduced in 12 and we give criteria on the density of the ordinary locus

affine grassmannians and the geometric satake in mixed characteristic we endow the set of lattices in q n p with a reasonable algebro geometric structure as a result we prove the representability of affine grassmannians and establish the geometric satake equivalence in mixed characteristic we also give an application of our theory to the study of rapoport zink spaces

affineness of deligne lusztig varieties for minimal length elements abstract we prove that the deligne lusztig varieties associated to elements of the weyl group which are of minimal length in their twisted class are affine our proof differs from the proof of he and orlik rapoport and it is inspired by the case of regular elements which correspond to the varieties involved in broue s conjectures

the g stable pieces of the wonderful compactification let g be a connected simple algebraic group over an algebraically closed field there is a partition of the wonderful compactification of into finite many g stable pieces which was introduced by lusztig in this paper we will investigate the closure of any g stable piece in we will show that the closure is a disjoint union of some g stable pieces which was first conjectured by lusztig we will also prove the existence of cellular decomposition if the closure contains finitely many orbits

on approximately higher ring derivations abstract in this paper we examine the hyers ulam the isac and rassias type stability and the bourgin type superstability of a functional inequality corresponding to the following functional equation respectively f n x y i 0 n f i x f n i y in particular an additive operator satisfying the above equation is said to be a ring homomorphism respectively a ring derivation if n 0 respectively n 1 and f 0 is an identity operator

kazhdan lusztig immanants and products of matrix minors abstract using the kazhdan lusztig basis c w 1 w s n for the symmetric group algebra we obtain nonnegativity properties of certain polynomials in matrix minors in particular we show that the application of these polynomials to jacobi trudi matrices yields symmetric functions which are equal to nonnegative linear combinations of schur functions

a subalgebra of 0 hecke algebra let w i be a finite coxeter group in the case where w is a weyl group berenstein and kazhdan in a berenstein d kazhdan geometric and unipotent crystals ii from unipotent bicrystals to crystal bases in quantum groups in contemp math vol 433 amer math soc providence ri 2007 pp 13 88 constructed a monoid structure on the set of all subsets of i using unipotent linear bicrystals in this paper we will generalize this result to all types of finite coxeter groups including non crystallographic types our approach is more elementary based on some combinatorics of coxeter groups moreover we will calculate this monoid structure explicitly for each type

on the flatness of models of certain shimura varieties of pel type consider a pel shimura variety associated to a unitary group that splits over an unramified extension of q p rapoport and zink have defined a model of the shimura variety over the ring of integers of the completion of the reflex field at a place lying over p with parahoric level structures at p we show that this model is flat as conjectured by rapoport and zink and that its special fibre is reduced

character sheaves on certain spherical varieties abstract we study a class of perverse sheaves on some spherical varieties which include the strata of the de concini procesi completion of a symmetric variety this is a generalization of the theory of parabolic character sheaves

topological flatness of local models in the ramified case local models are schemes defined in terms of linear algebra which can be used to study the local structure of integral models of certain shimura varieties with parahoric level structure we investigate the local models for groups of the form open image in new window is a totally ramified extension as defined by pappas and rapoport and show that they are topologically flat in the linear case flatness can be deduced from this

the supersingular locus in siegel modular varieties with iwahori level structure we study moduli spaces of abelian varieties in positive characteristic more specifically the moduli space of principally polarized abelian varieties on the one hand and the analogous space with iwahori type level structure on the other hand we investigate the ekedahl oort stratification on the former the kottwitz rapoport stratification on the latter and their relationship in this way we obtain structural results about the supersingular locus in the case of iwahori level structure for instance a formula for its dimension in case g is even

integral crystalline cohomology over very ramified valuation rings in this paper we intend to show how fontaine s comparison theory fol fo2 between crystalline and p adic etale cohomology can be extented to very ramified base rings so far it had been developed either for qp coefficients or zp coefficients if the base is unramified over the witt vectors see fa2 for example it states that for any p adic discrete valuation ring v there exists a ring b v with the following property if x denotes a smooth and proper v scheme the p adic etale cohomology of the generic fiber x xv k is related to the crystalline cohomology of x v0 vo defined below by an isomorphism

mod points on shimura varieties of abelian type we show that the mod p points on a shimura variety of abelian type with hyperspecial level have the form predicted by the conjectures of kottwitz and langlands rapoport along the way we show that the isogeny class of a mod p point contains the reduction of a special point

explicit formulae for the brenti s polynomials γa1 ar abstract we introduce two kinds of generalized catalan numbers a b a b z and a1 ar h a i p h n they can be interpreted as the numbers of certain bounded lattice paths in a lattice point set n n 1 three explicit formulae for the brenti s polynomials a1 ar are given in terms of generalized catalan numbers by these formulae we study the properties of a1 ar and answer some problems of brenti

codimensions of newton strata for sl3 f in the iwahori case we study the newton stratification on sl 3 f where f is a laurent power series field we provide a formula for the codimensions of the newton strata inside each component of the affine bruhat decomposition on sl 3 f these calculations are related to the study of certain affine deligne lusztig varieties in particular we describe a method for determining which of these varieties is non empty in the case of sl 3 f

minimal length elements of coxeter groups let w be a coxeter group and wj a finite parabolic subgroup we present here a geometric new proof of x he s result on minimal length elements of an orbit of wj which acts on w in a certain way

decomposition matrices for low rank unitary groups we study the decomposition matrices of the unipotent blocks of finite special unitary groups sun q for unitary primes larger than n up to few unknown entries we give a complete solution for n 2 10 we also prove a general result for two column partitions when divides q 1 this is achieved using projective modules coming from the adic cohomology of deligne lusztig varieties

ideal triangles in euclidean buildings and branching to levi subgroups abstract let g denote a connected reductive group defined and split over z and let m g denote a levi subgroup in this paper we study varieties of geodesic triangles with fixed vector valued side lengths in the bruhat tits buildings associated to g along with varieties of ideal triangles associated to the pair m g the ideal triangles have a fixed side containing a fixed base vertex and a fixed infinite vertex such that other infinite side containing has fixed ideal length and the remaining finite side has fixed length we establish an isomorphism between varieties in the second family and certain varieties in the first family the pair and the triple satisfy a certain relation we apply these results to the study of the hecke ring of g and the restriction homomorphism r g r m between representation rings we deduce some new saturation theorems for constant term coefficients and for the structure constants of the restriction homomorphism

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

combinatorial properties of the kazhdan lusztigr polynomials forsn abstract we point out a deep and surprising connection between the kazhdan lusztigr polynomials forsnand the enumeration and combinatorics of increasing subsequences in permutations this leads to a simple combinatorial recurrence and to several new closed formulas for these polynomials

ekedahl oort and newton strata for shimura varieties of pel type we study the ekedahl oort stratification for good reductions of shimura varieties of pel type these generalize the ekedahl oort strata defined and studied by oort for the moduli space of principally polarized abelian varieties the siegel case they are parameterized by certain elements w in the weyl group of the reductive group of the shimura datum we show that for every such w the corresponding ekedahl oort stratum is smooth quasi affine and of dimension ell w and in particular non empty some of these results have previously been obtained by moonen vasiu and the second author using different methods we determine the closure relations of the strata we give a group theoretical definition of minimal ekedahl oort strata generalizing oort s definition in the siegel case and study the question whether each newton stratum contains a minimal ekedahl oort stratum as an interesting application we determine which newton strata are non empty this criterion proves conjectures by fargues and by rapoport generalizing a conjecture by manin for the siegel case we give a necessary criterion when a given ekedahl oort stratum and a given newton stratum meet

topological flatness of orthogonal local models in the split even case i local models are schemes defined in terms of linear algebra that were introduced by rapoport and zink to study the etale local structure of integral models of certain pel shimura varieties over p adic fields a basic requirement for the integral models or equivalently for the local models is that they be flat in the case of local models for even orthogonal groups genestier observed that the original definition of the local model does not yield a flat scheme in a recent article pappas and rapoport introduced a new condition to the moduli problem defining the local model the so called spin condition and conjectured that the resulting spin local model is flat we prove a preliminary form of their conjecture in the split iwahori case namely that the spin local model is topologically flat an essential combinatorial ingredient is the equivalence of admissibility and permissibility for two minuscule cocharacters in root systems of type d

connected components of closed affine deligne lusztig varieties for rese fgln abstract let f be a p adic field and let e f be a finite unramified extension for the weil restriction res e f g l n of the general linear group g l n we determine the connected components of closed affine deligne lusztig varieties of arbitrary parahoric level

the character sheaves on the group compactification abstract we give a definition of character sheaves on the group compactification which is equivalent to lusztig s definition in g lusztig parabolic character sheaves ii mosc math j 4 4 2004 869 896 we also prove some properties of the character sheaves on the group compactification

vers le socle localement analytique pour mathrm gl _n ii on conjecture que certaines representations localement mathbb q p analytiques irreductibles de mathrm gl n l pour l mathbb q p infty apparaissent en sous objet dans des espaces hecke isotypiques de formes automorphes p adiques lorsque l mathbb q p on demontre quelques resultats partiels dans la direction de cette conjecture en utilisant des resultats recents sur les varietes de hecke et une nouvelle formule d adjonction pour le foncteur localement analytique de jacquet emerton

formulae relating the bernstein and iwahori matsumoto presentations of an affine hecke algebra abstract we consider the anti dominant variants of the elements occurring in the bernstein presentation of an affine hecke algebra h we find explicit formulae for in terms of the iwahori matsumoto generators tw w ranging over the extended affine weyl group of the root system r in the case i r is arbitrary and is a minuscule coweight or ii r is attached to gln and mek where ek is a standard basis vector and m 1 in the above cases certain minimal expressions for play a crucial role such minimal expressions exist in fact for any coweight for gln we give a sheaf theoretic interpretation of the existence of a minimal expression for the corresponding perverse sheaf on the affine schubert variety x t is the push forward of an explicit perverse sheaf on the demazure resolution m x t x t this approach yields for a minuscule coweight of any r or for an arbitrary coweight of gln a conceptual albeit less explicit expression for the coefficient w of the basis element tw in terms of the cohomology of a fiber of the demazure resolution

pro p iwahori hecke algebra and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring h 1 of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring h 1 is finitely generated as a module over its centre these results are proved in 12 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of h 1 to k which is as null as possible will be called null the simple h k modules with a null central character are called supersingular when g gl n we show that each simple h k module of dimension n containing a character of the affine subring h aff is supersingular the proof uses the minimal expressions of haines generalized to h 1 and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 11 and when n 3 rachel ollivier

some results on stability of extended derivations abstract in this paper we prove the generalized hyers ulam rassias stability of extended derivations on unital banach algebras associated to a generalized jensen equation

on the stability of an n dimensional cubic functional equation abstract let n 2 be an integer number in this paper we investigate the generalized hyers ulam rassias stability in banach spaces and also banach modules over a banach algebra and a c algebra and the stability using the alternative fixed point of an n dimensional cubic functional equation in banach spaces f j 1 n 1 x j 2 x n f j 1 n 1 x j 2 x n j 1 n 1 f 2 x j 2 f j 1 n 1 x j 4 j 1 n 1 f x j x n f x j x n

the jordan holder series for nearby cycles on some shimura varieties and affine flag varieties we study the jordan holder series for nearby cycles on certain shimura varieties and rapoport zink local models and on finite dimensional pieces of beilinson s deformation of the affine grassmannian to the affine flag variety and their p adic analogues we give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups and we also provide an algorithm to compute multiplicities in terms of the affine hecke algebra msc classification 14m15 14g35 20c08

on the affineness of deligne lusztig varieties abstract we prove that the deligne lusztig variety associated to minimal length elements in any conjugacy class of the weyl group is affine which was conjectured by orlik and rapoport in s orlik m rapoport deligne lusztig varieties and period domains over finite fields arxiv 0705 1646

green polynomials of weyl groups elliptic pairings and the extended dirac index abstract in this paper we give a uniform construction of irreducible genuine characters of the pin cover w of a weyl group w and put them into the context of theory of springer representations in the process we provide a direct connection between springer theory via green polynomials the irreducible representations of w and an extended dirac operator for graded hecke algebras we also introduce a q elliptic pairing for w with respect to the reflection representation v these constructions are of independent interest the q elliptic pairing is a generalization of the elliptic pairing of w introduced by reeder and it is also related to s kato s notion of graded kostka systems for the semidirect product a w c w s v

fundamental elements of an affine weyl group fundamental elements are certain special elements of affine weyl groups introduced by gortz haines kottwitz and reuman they play an important role in the study of affine deligne lusztig varieties in this paper we obtain characterizations of the fundamental elements and their natural generalizations we also derive an inverse to a version of newton hodge decomposition in affine flag varieties as an application we obtain a group theoretic generalization of oort s results on minimal p divisible groups and we show that in certain good reduction of pel shimura datum each newton stratum contains a minimal ekedahl oort stratum this generalizes a result of viehmann and wedhorn

on the hodge newton filtration for p divisible o modules the notions hodge newton decomposition and hodge newton filtration for f crystals are due to katz and generalize messing s result on the existence of the local etale filtration for p divisible groups recently some of katz s classical results have been generalized by kottwitz to the context of f crystals with additional structures and by moonen to ordinary p divisible groups in this paper we discuss further generalizations to the situation of crystals in characteristic p and of p divisible groups with additional structure by endomorphisms

on the μ admissible set in the extended affine weyl groups of e6 and e7 giving explicit examples we show that the admissible set and the permissible set do not agree for non trivial minuscule coweights in the cases of e6 and e7

connected components of closed affine deligne lusztig varieties for split reductive algebraic groups we determine the sets of connected components of closed affine deligne lusztig varieties with parahoric level structure

boolean elements in kazhdan lusztig theory abstract kazhdan lusztig polynomials have been proven to play an important role in different fields despite this there are still few explicit formulae for them here we give closed product formulae for the kazhdan lusztig polynomials indexed by boolean elements in a class of coxeter systems that we call linear boolean elements are elements smaller than a reflection that admits a reduced expression of the form s 1 s n 1 s n s n 1 s 1 s i s s i s j if i j then we provide several applications of this result concerning the combinatorial invariance of the kazhdan lusztig polynomials the classification of the pairs u v with u v the kazhdan lusztig elements and the intersection homology poincare polynomials of the schubert varieties

character sheaves on the semi stable locus of a group compactification abstract we study the intermediate extension of the character sheaves on an adjoint group to the semi stable locus of its wonderful compactification we show that the intermediate extension can be described by a direct image construction as a consequence we show that the ordinary restriction of a character sheaf on the compactification to a semi stable stratum is a shift of semisimple perverse sheaf and is closely related to lusztig s restriction functor from a character sheaf on a reductive group to a direct sum of character sheaves on a levi subgroup we also provide a conjectural formula for the boundary values inside the semi stable locus of an irreducible character of a finite group of lie type which gives a partial answer to a question of springer 2006 21 this formula holds for steinberg character and characters coming from generic character sheaves in the end we verify lusztig s conjecture lusztig 2004 16 12 6 inside the semi stable locus of the wonderful compactification

centralizers of iwahori hecke algebras to date integral bases for the centre of the iwahori hecke algebra of a finite coxeter group have relied on character theoretical results and the isomorphism between the iwahori hecke algebra when semisimple and the group algebra of the finite coxeter group in this paper we generalize the minimal basis approach of f1 to provide a way of describing and calculating elements of the minimal basis for the centre of an iwahori hecke algebra which is entirely combinatorial in nature and independent of both the above mentioned theories this opens the door to further generalization of the minimal basis approach to other cases in particular we show that generalizing it to centralizers of parabolic subalgebras requires only certain properties in the coxeter group we show here that these properties hold for groups of type a and b giving us the minimal basis theory for centralizers of any parabolic subalgebra in these types of iwahori hecke algebra

alcoves associated to special fibers of local models the special fiber of the local model of a pel shimura variety with iwahori type level structure admits a cellular decomposition the set of strata is in a natural way a finite subset of the affine weyl group determined by the shimura data in this paper we generalize and give a new proof of a theorem of kottwitz and rapoport concerning the description of this set for the case of linear and symplectic groups for higher rank groups not of type an we produce counterexamples showing the situation is not as nice in general we also recover a theorem of deodhar characterizing the bruhat order on sn the local geometry can be approached using the rapoport zink local model m j 13 this protective op scheme is a local model for the singularities in the special fiber of sh g x9 k 9 but it is defined in terms of the pair g p using linear algebra and is somewhat easier to deal with than the shimura variety itself in this paper we address certain combinatorial questions which arise in the study of the special fiber m f of m to fix ideas consider the case where g is split it turns out that m f can be regarded as a finite dimensional union of iwahori orbits in the affine flag variety for g fp t see 5 and 8 it follows that m f has a stratification indexed by a finite set perm p of the extended affine weyl group w g for g equivalently perm p can be regarded as a finite set of alcoves in the affine coxeter complex determined by a splitting for g let wo denote the finite weyl group of g for each translation in the wo orbit

minimal length elements in some double cosets of coxeter groups abstract we study the minimal length elements in some double cosets of coxeter groups and use them to study lusztig s g stable pieces and the generalization of g stable pieces introduced by lu and yakimov we also use them to study the minimal length elements in a conjugacy class of a finite coxeter group and prove a conjecture in m geck s kim g pfeiffer minimal length elements in twisted conjugacy classes of finite coxeter groups j algebra 229 2 2000 570 600

on classification of σq conjugacy classes of a loop group abstract let k be an algebraically closed field and l k the field of laurent series over k let g be a connected reductive group over k such that the characteristic of k does not divide the order of the weyl group of g for q k the automorphism of l defined by a i i a i q i induces an automorphism q of the loop group g l we show that when q is not a root of unity the classification of q conjugacy classes of g l can be reduced to the classification of unipotent classes of non connected reductive groups as an application we recover the classification of q conjugacy classes for g g l n

weight elimination in serre type conjectures we prove the weight elimination direction of the serre weight conjectures as formulated by herzig for forms of u n which are compact at infinity and split at places dividing p in generic situations that is we show that all modular weights for a mod p galois representation are contained in the set predicted by herzig under some additional hypotheses we also show modularity of all the obvious weights

topological flatness of local models for ramified unitary groups i the odd dimensional case abstract local models are certain schemes defined in terms of linear algebraic moduli problems which give etale local neighborhoods of integral models of certain p adic pel shimura varieties defined by rapoport and zink when the group defining the shimura variety ramifies at p the local models and hence the shimura models as originally defined can fail to be flat and it becomes desirable to modify their definition so as to obtain a flat scheme in the case of unitary similitude groups whose localizations at q p are ramified quasi split gu n pappas and rapoport have added new conditions the so called wedge and spin conditions to the moduli problem defining the original local models and conjectured that their new local models are flat we prove a preliminary form of their conjecture namely that their new models are topologically flat in the case n is odd

geometric and homological properties of affine deligne lusztig varieties this paper studies ane deligne lusztig varieties x w b in the ane ag variety of a quasi split tamely ramied group we describe the geometric structure of x w b for a minimal length element w in the conjugacy class of an extended ane weyl group we then provide a reduction method that relates the structure of x w b for arbitrary elements w in the extended ane weyl group to those associated with minimal length elements based on this reduction we establish a connection between the dimension of ane deligne lusztig varieties and the degree of the class polynomial of ane

lifting of elements of weyl groups abstract suppose g is a reductive algebraic group t is a cartan subgroup of g n norm t and w n t is the weyl group if w w has order d it is natural to ask about the orders lifts of w to n it is straightforward to see that the minimal order of a lift of w has order d or 2d but it can be a subtle question which holds we first consider the question of when w itself lifts to a subgroup of n in which case every element of w lifts to an element of n of the same order we then consider two natural classes of elements regular and elliptic in the latter case all lifts of w are conjugate and therefore have the same order we also consider the twisted case

a perturbation of ring derivations on banach algebras abstract suppose a is a banach algebra and suppose f a a is an approximate ring derivation in the sense of hyers ulam rassias this stability phenomenon was introduced for the first time in the subject of functional equations by th m rassias th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300 if a has an approximate identity or if a is semisimple and commutative then we prove that f is an exact ring derivation

partial stabilities and partial derivations of n variable functions abstract we introduce the concepts of the partial derivations of a function from a normed algebra a 1 a n into a banach algebra b and prove the hyers ulam rassias stability of the function moreover we obtain some results about the applications of derivations such as the extended derivations and the approximately higher derivations

the image of a derivation is contained in the radical in 1955 i m singer and j wermer proved that a bounded derivation on a commutative banach algebra maps into the jacobson radical they conjectured that this result holds even if the derivation is unbounded we give a proof of this conjecture the central idea in the proof is the introduction of the concept of a recalcitrant system of elements in a commutative radical banach algebra such systems put algebraic constraints upon a derivation which prevent the derivation from mapping outside of the radical

pro p iwahori hecke ring and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring open image in new window of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring open image in new window is finitely generated as a module over its centre these results are proved in 11 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of open image in new window to k which is as null as possible will be called null the simple open image in new window modules with a null central character are called supersingular when g gl n we show that each simple open image in new window module of dimension n containing a character of the affine subring open image in new window is supersingular using the minimal expressions of haines generalized to open image in new window and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 10 and when n 3 rachel ollivier

connected components of closed affine deligne lusztig varieties we determine the set of connected components of closed affine deligne lusztig varieties for special maximal compact subgroups of split connected reductive groups we show that there is a transitive group action on this set thus such an affine deligne lusztig variety has isolated points if and only if its dimension is 0 we also obtain a description of the set of these varieties that are zero dimensional

computing the alternating trace of frobenius on the sheaves of nearby cycles on local models for gl4 and gl5 abstract consider a shimura variety defined over some number field and assume we have a model over the ring of integers at some prime of bad reduction it is then interesting to know the alternating trace of frobenius on the invariants under the inertia group of the sheaf of nearby cycles since these traces are related to the local factor of the hasse weil zeta function in this article we compute the semi simple alternating trace of frobenius for shimura varieties associated to the groups gu 2 2 and gu 3 2 with level structure of iwahori type by investigating the equations of the local model defined by rapoport and zink and by performing explicit blowing ups