✦ LIBER ✦
Torsion subgroups of Brauer groups and extensions of constant local degree for global function fields
✍ Scribed by Cristian D. Popescu
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 175 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
We show that, for all characteristic p global fields k and natural numbers n 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.