4 papers
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 some finiteness results for unramified cohomology
Igor A. Rapinchuk
We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically…
The genus of a division algebra and the unramified Brauer group
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
Let D be a finite-dimensional central division algebra over a field K. We define the genus gen(D) of D to be the collection of classes in the Brauer group of K represented by centr…