Related papers: Relative representability and parahoric level stru…

In this paper, we introduce the notions of parabolic representation pair variety and relative representation variety of a given parabolic type. We investigate the local behavior of these varieties. The Zariski tangent space and the tangent…

We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…

Let G be a unitary group over the rationals, associated to a CM-field F with totally real part F^+, with signature (1,1) at all the archimedean places of F^+. Under certain hypotheses on F^+, we show that Jacquet-Langlands correspondences…

We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified…

We extend the analysis of the Vafa $\mathcal{N}=4$ SUSY model of FQHE and discuss other observables which characterize the FQHE topological order. We consider in particular the braiding properties of quasi-holes with generic charge. As one…

We give a new proof of the existence of Klyachko models for unitary representations of ${\rm GL}_{n}(F)$ over a non-archimedean local field $F$. Our methods are purely local and are based on studying distinction within the class of ladder…

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We resolve a serious deficit in the existing theory by constructing a good notion of equivariant presheaves, with a suitable equivariant…

In this article we prove several level lowering results for cuspidal automorphic representations occurring in the cohomology of the Siegel modular threefold with paramodular level structure by adapting a method of Ribet in his proof of the…

Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of residual characteristic $p$. We classify the smooth, irreducible, admissible genuine mod-$p$ representations of the twofold metaplectic cover…

This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…

We use homological methods to establish a formal criterion for Generic Vanishing, in the sense originated by Green and Lazarsfeld and pursued further by Hacon and the first author, but in the context of an arbitrary Fourier-Mukai…

We review the analog of Fontaine's theory of crystalline $p$-adic Galois representations and their classification by weakly admissible filtered isocrystals in the arithmetic of function fields over a finite field. There crystalline Galois…

We explain how the geometric framework introduced in arXiv:2508.11621 [math.AG] provides a universal property for the 2-rings of perfect complexes on qcqs spectral or Dirac spectral schemes. As an application, given a qcqs spectral or Dirac…

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field to the category of L-modules, to the case where L is a field…

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on…

We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale…

We develop a theory of microlocalization for Harish-Chandra modules, adapting a construction of Losev (\cite{Losev2011}). We explore the applications of this theory to unipotent representations of real reductive groups. For complex groups,…

We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as the test function conjecture of Haines--Kottwitz in this framework. To this end, we establish a…

In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a…

We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra \g and the resonance varieties R(V,K)\subset V^* attached to irreducible \g-modules V and submodules K\subset V\wedge V. In the…