Tensor products of division algebras and fields

JOURNAL OF ALGEBRA

卷:394

Article

Rowen, Louis¹  Saltman, David J.² 

[1] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

[2] Ctr Commun Res, Princeton, NJ 08540 USA

关键词: Division algebra;    Schur index;    Ramification;    Picard group;    Brauer group;   

DOI  :  10.1016/j.jalgebra.2013.07.019

来源: Elsevier

【 摘 要 】

This paper began as an investigation of the question of whether D-1 circle times(F) D-2 is a domain where the D-i are division algebras and F is an algebraically closed field contained in their centers. We present an example where the answer is no, and also study the Picard group and Brauer group properties of F-1 circle times(F) F-2 where the F-i are fields. Finally, as part of our example, we have results about division algebras and Brauer groups over curves. Specifically, we give a splitting criterion for certain Brauer group elements on the product of two curves over F. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free