Related papers: Un cas PEL de la conjecture de Kottwitz
This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the…
In this paper we give a proof of the Bloch-Kato conjecture relating motivic cohomology and etale cohomology. It is a corrected version of the paper with the same title which posted earlier.
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 a conjecture of Pappas and Rapoport about the existence of ''canonical'' integral models of Shimura varieties of Hodge type with quasi-parahoric level structure at a prime $p$. For these integral models, we moreover show…
We study unramified unitary and unitary similitude groups in an odd number of variables. Using work of the first and third named authors on the Kottwitz Conjecture for the similitude groups, we show that the Fargues--Scholze local Langlands…
This paper proves the general rank one case of Dwork's conjecture over the affine space. It generalizes and improves the method of ANT-0141 "Dwork's conjecture on unit root zeta functions" (Ann. Math., 150(1999), 867-929). In addition,…
In this article, we pursue the study begun in \cite{Lup02} on the cohomology of rationally elliptic coformal spaces. Consequently, we complete, for such spaces, the proof of Lupton's conjecture and deduce Hilali's.
In his work on defining the pointed set B(G) for all local and global fields, Kottwitz introduced certain Galois gerbes and considered their 'algebraic' cohomology with values in algebraic groups. However, the gerbes so constructed are only…
We construct flat integral moduli schemes of PEL type D and the corresponding flat orthogonal Rapoport--Zink spaces with parahoric level structure over a $p$-adic integer ring. The construction relies on proving a conjecture of…
We prove some cases of the Zilber-Pink conjecture on unlikely intersections in Shimura varieties. Firstly, we prove that the Zilber-Pink conjecture holds for intersections between a curve and the union of the Hecke translates of a fixed…
We prove a Cohen-Dimca-Orlik type theorem for rank one $\mathbb{Z}$-local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S. Sugawara.
Let X be a compact connected Riemann surface of genus at least two. We compute the Chen--Ruan cohomology ring of the moduli space of stable PSL(2, C)--bundles of nontrivial second Stiefel--Whitney class over X.
In this article, we prove that a version of Tate conjectures for certain Deligne-Lusztig varieties implies the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level at unramified primes. Furthermore, we prove…
We elaborate the theory of the stable Bernstein center of a $p$-adic group $G$, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This conjecture provides a framework by…
We prove that the Jacquet-Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz's conjecture for Shimura varieties attached to unitary similitude…
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…
In this work, we study the supersingular locus of the Shimura variety associated to the unitary group $\mathrm{GU}(2,4)$ over a ramified prime. We show that the associated Rapoport-Zink space is flat, and we give an explicit description of…
We compare the conjecture of Buzzard-Gee on the association of Galois representations to C-algebraic automorphic representations with the conjectural description of the cohomology of Shimura varieties due to Kottwitz, and the reciprocity…
Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their "group-theoretic models" -- generalized affine Deligne-Lusztig varieties -- in cases where they have a particularly…
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…