On the size of the genus of a division algebra

On the size of the genus of a division algebra

Let D be a central division algebra of degree n over a field K . One defines the genus gen( D ) as the set of classes [ D ′] ∈ Br( K ) in the Brauer group of K represented by central division algebras D ′ of degree n over K having the same maximal subfields as D . We prove that if the field K is fin...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics Vol. 292; no. 1; pp. 63 - 93
Main Authors: Chernousov, Vladimir I., Rapinchuk, Andrei S., Rapinchuk, Igor A.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 2016
Subjects:
Mathematics
Mathematics and Statistics
STEKLOV Institute
Exact Sequence
Galois Extension
Division Algebra
Good Reduction
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let D be a central division algebra of degree n over a field K . One defines the genus gen( D ) as the set of classes [ D ′] ∈ Br( K ) in the Brauer group of K represented by central division algebras D ′ of degree n over K having the same maximal subfields as D . We prove that if the field K is finitely generated and n is prime to its characteristic, then gen( D ) is finite, and give explicit estimations of its size in certain situations.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543816010053