Related papers: Unramified representations of reductive groups ove…

We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we…

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…

Let $\mathfrak{o}$ be the ring of integers in a non-Archimedean local field with finite residue field, $\mathfrak{p}$ its maximal ideal, and $r\geq2$ an integer. An irreducible representation of the finite group…

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

This paper proves the existence of cuspidal automorphic forms for a reductive group, invariant under an automorphism of finite order. The techniques used are a local analysis of orbital integrals and the Arthur-Selberg trace formula.

Inspired by Ol'shanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We then look at the applications to certain…

Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…

We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof we use realisations of characters in $\ell$-adic…

We prove a conjecture of Broue about the Jordan decomposition of blocks of finite reductive groups. We show that a block of a finite connected reductive group, in non-describing characteristic, is Morita-equivalent to a quasi-isolated block…

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…

An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular. Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional local…

For an arbitrary non-archimedean local field we classify reductive group schemes over the corresponding Fargues-Fontaine curve by group schemes over the category of isocrystals. We then classify torsors under such reductive group schemes by…

In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

This paper is a summary of author's results on finite flat commutative group schemes. The properties of the generic fibre functor are discussed. A complete classification of finite local flat commutative group schemes over mixed…

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…