Torsion subgroups of Brauer groups and extensions of constant local degree for global function fields

JOURNAL OF NUMBER THEORY

卷:115

Article

Popescu, CD

关键词: Brauer groups;    class field theory;    function fields;   

DOI  :  10.1016/j.jnt.2004.07.002

来源: Elsevier

【 摘 要 】

We show that, for all characteristic p global fields k and natural numbers 17 coprime to the order,of the non-p-part of the Picard group Pic(0)(k) of k, there exists an abelian extension L/k whose local degree at every prime of k is equal to n. This answers in the affirmative in this context a question recently posed by Kisilevsky and Sonn. As a consequence, we show that, for all n and k as above, the n-torsion subgroup Br-n(k) of the Brauer group Br(k) of k is algebraic, answering a question of Aldjaeff and Sonn in this context. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free