Related papers: Langlands parameters for reductive groups over fin…

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…

A relative one-relator presentation has the form P = < X,H ; R > where X is a set, H is a group, and R is a group word on X and H. We show that if the group word on X obtained from R by deleting all the terms from H has what we call the…

We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide explicit bounds for orders of finite subgroups of automorphism groups of…

Let $K$ be a number field with ring of integers $\mathcal{O}_K$. We describe and classify finite, flat, and linearly reductive subgroup schemes of $\mathrm{SL}_2$ over $\mathrm{Spec}\:\mathcal{O}_K$. We also establish finiteness results for…

After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…

We give a description of the Picard group of a reductive group over a number field as an abelianized Galois cohomology group. It gives another approach of a result due to Labesse.

We prove a version of the twisted geometric Satake equivalence and extend the Langlands parametrization of V. Lafforgue to certain covers of reductive groups.

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.

In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and S\'{a}rk\"{o}zy and Shparlinski.

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over…

We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any…

This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.

In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is isomorphic to some algebra over a finite base. This result…

This expository note introduces a normalization of the indexing of the lower and upper numbering ramification subgroups of local class field theory. We then look at how this normalization interacts with base change for Langlands parameters.

The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.

We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…

In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

In this paper we introduce another finite field analogue for Appell series F_{1} and obtain certain reduction formulae and a generating function for this analogue.