Igor A. Rapinchuk

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

Showing 2023Show all

2 papers · 1 filter

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 $K$ 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 \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…