activity
20092026
most citedOn linear representations of Chevalley groups over commutative rings

16 citations · 42 across the 21 of their papers we have counts for

collaborators

28 papers

math.GR2026

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…

math.NT2026

Finiteness of the Tate-Shafarevich group over function fields for groups of multiplicative type

Igor A. Rapinchuk, Avinash Roy

Let be the function field of a smooth geometrically integral variety of dimension over a field of characteristic 0 and be the set of discrete valuat…

math.NT2023

The finiteness of the Tate-Shafarevich group over function fields for algebraic tori defined over the base field

Andrei S. Rapinchuk, Igor A. Rapinchuk

Let be a field and be a set of rank one valuations of . The corresponding Tate-Shafarevich group of a -torus is $Sha(T , V) = \ker\left(H^1(K , T) \to \prod_{v \i…

math.RA2023

Residue maps, Azumaya algebras, and buildings

Igor A. Rapinchuk

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 ac…

math.GR2022

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…

math.GR2022

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…