16 citations · 42 across the 21 of their papers we have counts for
11 papers · 1 filter
Products of trees and -torsors over the punctured affine line
Andrei S. Rapinchuk, Igor A. Rapinchuk, Avinash Roy
The goal of this article is to present a computation of the Galois cohomology of the group over rings of Laurent polynomials. This computation recovers the mai…
Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings
Peter Abramenko, Andrei S. Rapinchuk, Igor A. Rapinchuk
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 with good reduction and the genus problem
Igor A. Rapinchuk
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…
On abstract homomorphisms of some special unitary groups
Igor A. Rapinchuk, Joshua Ruiter
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…
On abstract homomorphisms of Chevalley groups over the coordinate rings of affine curves
Igor A. Rapinchuk
The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of comm…
On abstract representations of the groups of rational points of algebraic groups in positive characteristic
Mitya Boyarchenko, Igor A. Rapinchuk
We analyze the structure of a large class of connected algebraic rings over an algebraically closed field of positive characteristic using Greenberg's perfectization functor. We th…
On the character varieties of finitely generated groups
Igor A. Rapinchuk
We establish three results dealing with the character varieties of finitely generated groups. The first two are concerned with the behavior of as a function of , a…
Abstract homomorphisms of algebraic groups and applications
Igor A. Rapinchuk
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geomet…
On abstract representations of the groups of rational points of algebraic groups and their deformations
Igor A. Rapinchuk
In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank First, we extend our earlier methods to analyze repre…
Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank >1 over noetherian rings
Andrei S. Rapinchuk, Igor A. Rapinchuk
We prove the centrality of the congruence kernel for the elementary subgroup of a Chevalley group G of rank >1 over an arbitrary noetherian ring R (under some minor restrictions on…
On linear representations of Chevalley groups over commutative rings
Igor A. Rapinchuk
Let be the universal Chevalley-Demazure group scheme corresponding to a reduced irreducible root system of rank , and let be a commutative ring. We analyze the line…