Rational maps between varieties associated to central simple algebras

[摘要] In this paper we show that there exist rational maps between varieties associated to isomorphism classes of central simple algebras such as Severi-Brauer varieties, norm hypersurfaces and symmetric powers, provided the Brauer-equivalence classes of the algebras involved generate the same cyclic subgroup in Br(k). In some cases we even get rational embed-dings. We relate the obtained results to the Amitsur conjecture. (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Central simple algebras;Severi-Brauer varieties;Norm varieties;Symmetric powers;Rational maps