Related papers: On the Bernstein--Zelevinsky classification in fam…

In this paper, we first prove a local family version of the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, then we extend the famous Witten's rigidity Theorems to the family case. Several family vanishing theorems for elliptic…

We prove $p$-adic versions of a classical result in arithmetic geometry stating that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of…

We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a…

We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for…

Let F be a non-archimedean local field and let $G^\sharp$ be the group of F-rational points of an inner form of $SL_n$. We study Hecke algebras for all Bernstein components of $G^\sharp$, via restriction from an inner form G of $GL_n (F)$.…

Zelevinsky's classification theory of discrete series of $p$-adic general linear groups has been well known. M{\oe}glin and Tadic gave the same kind of theory for $p$-adic classical groups, which is more complicated due to the occurrence of…

The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…

We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…

We introduce a bounded version of Bredon cohomology for groups relative to a family of subgroups. Our theory generalizes bounded cohomology and differs from Mineyev--Yaman's relative bounded cohomology for pairs. We obtain cohomological…

In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GL(n,F) for a positive integer n and let R be an algebraically closed field of characteristic different from p. When R has…

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…

In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…

By means of the theory of strongly semistable sheaves and of the theory of the Greenberg transform, we generalize to higher dimensions a result on the sparsity of p-divisible unramified liftings which played a crucial role in Raynaud's…

We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of $p$-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes…

For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKay-quiver of a finite linearly reductive subgroup scheme of $SL(2)$. Moreover, for a normal subgroup…

Let p be an odd prime, K a finite extension of Q_p, G=Gal(\bar K/K) the Galois group and e=e(K/Q_p) the ramification index. Suppose T is a p^n torsion representation such that T is isomorphic to a quotient of two G-stable Z_p-lattices in a…

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the…

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in…