16 citations · 42 across the 21 of their papers we have counts for
6 papers · 1 filter
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…
The finiteness of the genus of a finite-dimensional division algebra, and some generalizations
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applic…
On the size of the genus of a division algebra
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) of K represented by central d…
Division algebras with the same maximal subfields
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We al…
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…
On division algebras having the same maximal subfields
A. S. Rapinchuk, I. A. Rapinchuk
We address the problem of when two finite dimensional central division algebras over the same field are necessarily isomorphic given that they have the same maximal subfields.