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Invariant Brauer group of an abelian variety
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Orr, Martin, Skorobogatov, A. N., Valloni, D. and Zarhin, Yu. G. (2022) Invariant Brauer group of an abelian variety. Israel Journal of Mathematics, 249 . pp. 695-733. doi:10.1007/s11856-022-2323-5 ISSN 0021-2172.
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Official URL: https://doi.org/10.1007/s11856-022-2323-5
Abstract
We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper bound on the rank. We exhibit many cases in which the invariant Brauer group is zero, and construct complex abelian varieties in every dimension starting with 2, both simple and non-simple, with invariant Brauer group of order 2. We also address the situation in finite characteristic and over non-closed fields.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Grothendieck groups, Brauer groups, Abelian varieties, Torus (Geometry), Complex manifolds | ||||||||
| Journal or Publication Title: | Israel Journal of Mathematics | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0021-2172 | ||||||||
| Official Date: | June 2022 | ||||||||
| Dates: |
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| Volume: | 249 | ||||||||
| Page Range: | pp. 695-733 | ||||||||
| DOI: | 10.1007/s11856-022-2323-5 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-022-2323-5 | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 1 April 2021 | ||||||||
| Date of first compliant Open Access: | 29 June 2023 | ||||||||
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