相关论文: Weight zero Eisenstein cohomology of Shimura varie…

A particular case of Bergeron-Venkatesh's conjecture predicts that torsion classes in the cohomology of Shimura varieties are rather rare. According to this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first associate to…

We prove that singular cohomology of the underlying space of Berkovich's analytification of a scheme $X$ locally of finite type over a trivially-valued field $k$ of characteristic $0$ is isomorphic to cdh-cohomology with integer…

This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian…

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…

We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…

This text contributes to the foundations of the theory of global Berkovich spaces, that is to say Berkovich spaces over Banach rings with nice properties such as $\mathbf{Z}$, rings of integers of number fields, discrete valuation rings,…

We show that the weight 0 part of the first cohomology of a complex algebraic variety $X$ is a topological invariant, and give an explicit description of its dimension using a topological construction of the normalization of $X$, where $X$…

This article proposes a new approach to studying the spectral Eisenstein series of weight $k$ on a congruence subgroup of $\text{SL}_2(\mathbb{Z})$ using Hecke's theory of Eisenstein series for the principal congruence subgroups. Our method…

We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of $P^N$ of small codimensions and of their preimages with respect to proper morphisms…

In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor's book, we describe the monodromy filtration of the vanishing cycles complex and the spectral sequence associated to it. We prove in…

We introduce K-theoretic Gromov-Witten invariants of algebraic orbifold target spaces. Using the methods developed by Givental-Tonita we characterize Giventals Lagrangian cone of quantum K theory of orbifolds in terms of the cohomological…

This article is a revised, short and english version of my PhD thesis. First, we show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to…

We prove that the intersection cohomology of the Baily-Borel compactification of a complex Shimura variety is identified with the top weight quotient of the mixed Hodge structure on the reductive Borel-Serre compactification. This yields…

This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review…

We formulate and prove a version of the arithmetic Siegel-Weil formula for (zero dimensional) Shimura varieties attached to tori, equipped with some additional data. More precisely, we define a family of ``special" divisors in terms of…

We show that the etale cohomology (with compact supports) of an algebraic variety $X$ over an algebraically closed field has the canonical weight filtration $W$, and prove that the middle weight part of the cohomology with compact supports…

Norm-compatible families of cohomology classes for Shimura varieties, and other arithmetic symmetric spaces, play an important role in Iwasawa theory of automorphic forms. The aim of this note is to give a systematic approach to proving…

This article is the $\mathrm{Z}_l$-version of my paper "Monodromie du faisceau pervers des cycles \'evanescents de quelques vari\'et\'es de Shimura simples" in Invent. Math. 2009 vol 177 pp. 239-280, where we study the vanishing cycles of…

We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are…