Related papers: Congruence relations for Shimura varieties associa…

We show that the Taylor-Wiles method can be applied to the cohomology of a Shimura variety $S$ of PEL type attached to a unitary similitude group $G$, with coefficients in the coherent sheaf attached to an automorphic vector bundle $\CF$ ,…

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $\mathbb{Q}_p$. To get this result, we use the analytic continuation…

Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…

We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.

Local models are schemes which are intended to model the \'etale-local structure of p-adic integral models of Shimura varieties. Pappas and Zhu have recently given a general group-theoretic construction of flat local models with parahoric…

We give an explicit version of Shimura's reciprocity law for singular values of Siegel modular functions. We use this to construct the first examples of class invariants of quartic CM fields that are smaller than Igusa invariants. Our…

We prove homology stability for elementary and special linear groups over rings with many units improving known stability ranges. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative…

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten…

Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit…

Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ over a non-archimedean local field $F$ of odd residue characteristic $p$. In this paper, for any supersingular representation of $G$ that contains the Steinberg weight, we prove its…

We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han…

We study the reduction of certain integral models of Shimura varieties of PEL type with Iwahori level structure. On these spaces we have the Kottwitz-Rapoport and the $p$-rank stratification. We show that the $p$-rank is constant on a KR…

A locally compact groupoid is said to be exact if its associated reduced crossed product functor is exact. In this paper, we establish some permanence properties of exactness, including generalizations of some known results for exact…

We respectfully reply to Wang et al.'s reply to our comment to their [JHEP $\textbf{09}$ (2021) 053]. Some more subtleties and details are discussed for hopefully better clarification and understanding, especially about the conditions in…

In this article, we prove results about the cohomology of compact unitary group Shimura varieties at split places. In nonendoscopic cases, we are able to give a full description of the cohomology, after restricting to integral Hecke…

We prove that under some conditions on the monodromy, families of abelian covers of the projective line do not give rise to (higher dimensional) Shimura subvarieties in $A_g$. This is achieved by a reduction to $p$ argument. We also use…

The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural…

Given a simple Lie group $G$, we show that the lattices in $G$ are weakly uniformly discrete. This is a strengthening of the Kazhdan-Margulis theorem. Our proof however is straightforward --- considering general IRS rather than lattices…

We study the intersections of special cycles on a unitary Shimura variety of signature (n-1,1), and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of…