Related papers: Potentially good reduction loci of Shimura varieti…

We prove that quantized multiplicative quiver varieties and quantum character varieties define sheaves of Azumaya algebras over the corresponding classical moduli spaces, and we prove that the Azumaya locus of the Kauffman bracket skein…

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations. For genus 2 we give a formula for the full Eisenstein…

In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for GU(1; n-1). We explicitly compute the global structure of the reduced locus of a single special cycle, as well as of an arbitrary…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

We generalize some classical results on Chow group of an abelian variety to semiabelian varieties and to motivic (co)homology, using a result of Ancona--Enright-Ward--Huber on a decomposition of the motive of a semiabelian variety in the…

We consider principally polarized abelian varieties with quaternionic multiplication over number fields and we study the field of moduli of their endomorphisms in relation to the set of rational points on suitable Shimura varieties.

The Eichler-Shimura isomorphism describes a certain cohomology group with coefficients in a space of polynomials by using holomorphic modular/cusp forms. It determines a canonical decomposition of the corresponding de Rham cohomology group…

We construct integral models of Shimura varieties of abelian type with parahoric level structure over odd primes. These models are \'etale locally isomorphic to corresponding local models.

In \textit{Shimuravariet\"{a}ten und Gerben} \cite{LR87}, Langlands and Rapoport developed the theory of pseudo-motivic Galois gerb and admissible morphisms between Galois gerbs, with a view to formulating a conjectural description of the…

We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by…

Let G be a connected reductive complex affine algebraic group, and let X denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in X, extending a theorem of Richardson and proving…

The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.

Level $m$-stratifications on PEL Shimura varieties are defined and studied by Wedhorn using BT-$m$s with PEL structure, and then by Vasiu for general Hodge type Shimura varieties using Shimura $F$-crystals. The theory of foliations is…

The paper provides a combinatorial method to decide when the space of local systems with non vanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of…

In this article we first survey the analogy between Shimura varieties (resp. Rapoport-Zink spaces) and moduli stacks for global G-shtukas (resp. Rapooprt Zink spaces for local P-shtukas). This part is intended to enrich the dictionary…

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be…

In this article we use a Prym construction to study low dimensional abelian varieties with an action of the quaternion group. In special cases we describe the Shimura variety parameterizing such abelian varieties, as well as a map to this…

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\nmid |\pi_1(\mathsf{G}^{\rm der})|$. Under some mild additional…

These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for…

In this article we introduce the local versions of the Voevodsky category of motives with Z/p-coefficients over a field k, parameterized by finitely-generated extensions of k. We introduce the, so-called, flexible fields, passage to which…