Related papers: Reductions of Hecke correspondences on Anderson mo…

We associate with every Renner monoid $R$ a \emph{generic Hecke algebra} $\H(R)$ over $\mathbb{Z}[q]$ which is a deformation of the monoid $\mathbb{Z}$-algebra of $R$. If $M$ is a finite reductive monoid with Borel subgroup $B$ and…

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of…

The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Picard surfaces with regular algebraic coefficients. As a consequence, we are able to define…

We show that Ramanujan-type congruences are preserved by the action of the shallow Hecke algebra and provide several structure results for them. We discover a dichotomy between congruences originating in Hecke eigenvalues and congruences on…

The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let's mention : (1) the control of the image of the Galois representation modulo $p$, (2) Hida's…

In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological…

The purpose of this article is to give an overview of the series of papers [BK1], [BK2] concerning the $p$-adic Beilinson conjecture of motives associated to Hecke characters of an imaginary quadratic field $K$, for a prime $p$ which splits…

We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of Higgs moduli spaces conjectured by Hausel and…

We show that the reduction mod p of an orthogonal linear representation is orthogonal, and we generalize this fact to representations of algebras with involution.The proofs make an essential use of the notion of " middle lattices ".

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…

The authors defined in "$h^1\ne h_1$ for Anderson t-motives" the notion of an affine equation associated to a t-motive $M$. Here we define two systems of affine equations associated to a t-motive $M$, used for calculation of $H^1(M)$ and…

We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, yielding congruences for their coefficients modulo powers of primes. As an application we derive systematic congruences for several higher-order…

We study the action of the derived Hecke algebra on the space of weight one forms. By analogy with the topological case, we formulate a conjecture relating this to a certain Stark unit. We verify the truth of the conjecture numerically, for…

We relate the dimensions of $L^p$ reduced cohomology spaces in degree k of an ALE manifold to the dimension of some spaces of decaying harmonic forms, depending both on p and on k. In this class of manifolds, this provides an extension to…

The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ have been classified except when $q=-1$. We prove one half of a conjecture which we believe classifies the reducible Specht modules when $q=-1$…

The first part of the paper is a survey of recent results about the cohomology of $(\phi,\Gamma)$-modules and its applications to the theory of Selmer complexes. In the second part we formulate a version of the Main Conjecture for $p$-adic…

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

We prove a number of unconditional statistical results of the Hecke coefficients for unitary cuspidal representations of $\operatorname{GL}(2)$ over number fields. Using partial bounds on the size of the Hecke coefficients, instances of…

We give a classification of the simple modules for the cyclotomic Hecke algebras over $\mathbb{C}$ in the modular case. We use the unitriangular shape of the decomposition matrices of Ariki-Koike algebras and Clifford theory.