Zobrazeno 1 - 10
of 92
pro vyhledávání: '"Rapinchuk, Igor A."'
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 8, Pp 939-944 (2021)
We present a number of finiteness results for algebraic tori (and, more generally, for algebraic groups with toric connected component) over two classes of fields: finitely generated fields and function fields of algebraic varieties over fields of ty
Externí odkaz:
https://doaj.org/article/2a6b6ae1f4d14ae1b7e22ef38dfbb8e7
Let $K$ be a field and $V$ be a set of rank one valuations of $K$. The corresponding Tate-Shafarevich group of a $K$-torus $T$ is $Sha(T , V) = \ker\left(H^1(K , T) \to \prod_{v \in V} H^1(K_v , T)\right)$. We prove that if $K = k(X)$ is the function
Externí odkaz:
http://arxiv.org/abs/2307.01185
Autor:
Rapinchuk, Igor A.
The goal of this note is to give an explicit formula for the residues of twists of the matrix algebra in terms of the twisting cocycle. Combined with the Fixed Point Theorem for actions of finite groups on affine buildings, this leads to a quick proo
Externí odkaz:
http://arxiv.org/abs/2303.03175
We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable, assuming that
Externí odkaz:
http://arxiv.org/abs/2208.09353
Autor:
Rapinchuk, Igor A.
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic groups and its
Externí odkaz:
http://arxiv.org/abs/2205.00273
Publikováno v:
In Journal of Algebra 15 October 2024 656:3-23
Autor:
Rapinchuk, Igor A.
Publikováno v:
In Journal of Pure and Applied Algebra October 2024 228(10)
We provide a new condition for an absolutely almost simple algebraic group to have good reduction with respect to a discrete valuation of the base field which is formulated in terms of the existence of maximal tori with special properties. This chara
Externí odkaz:
http://arxiv.org/abs/2112.04315
Autor:
Rapinchuk, Igor A., Ruiter, Joshua
We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a standard
Externí odkaz:
http://arxiv.org/abs/2107.07351
This is a companion paper to our previous work, where we proved the finiteness of the Tate-Shafarevich group for an arbitrary torus $T$ over a finitely generated field $K$ with respect to any divisorial set $V$ of places of $K$. Here, we extend this
Externí odkaz:
http://arxiv.org/abs/2104.14625