Zobrazeno 1 - 10
of 134
pro vyhledávání: '"Rapinchuk, Andrei"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G11, Pp 1249-1255 (2022)
We prove that for a number field $F$, the distribution of the points of a set $\Sigma \subset \mathbb{A}_F^n$ with a purely exponential parametrization, for example a set of matrices boundedly generated by semi-simple (diagonalizable) elements, is of
Externí odkaz:
https://doaj.org/article/c5025fd882d440ce838592cc7c0a62f1
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
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic $0$), which is known to admit far-reaching group-theoretic implications. We achieve complete answers to certain longs
Externí odkaz:
http://arxiv.org/abs/2308.14013
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
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
Publikováno v:
In Journal of Algebra 15 October 2024 656:3-23
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
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
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
Comment: To appear in the Notices of the AMS. arXiv admin note: text ove
Comment: To appear in the Notices of the AMS. arXiv admin note: text ove
Externí odkaz:
http://arxiv.org/abs/2101.09811
We prove that if a linear group $\Gamma \subset \mathrm{GL}_n(K)$ over a field $K$ of characteristic zero is boundedly generated by semi-simple (diagonalizable) elements then it is virtually solvable. As a consequence, one obtains that infinite $S$-a
Externí odkaz:
http://arxiv.org/abs/2101.09386