Invariant Brauer group of an abelian variety

authored by

Martin Orr, Alexei N. Skorobogatov, Domenico Valloni, Yuri G. Zarhin

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.

Organisation(s)

Riemann Center for Geometry and Physics

External Organisation(s)

University of Manchester
Imperial College London
Russian Academy of Sciences (RAS)
Pennsylvania State University

Type

Artikel

Journal

Israel journal of mathematics

Volume

249

Pages

695-733

No. of pages

39

ISSN

0021-2172

Publication date

06.2022

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Electronic version(s)

https://doi.org/10.48550/arXiv.2007.05473 (Access: Offen)
https://doi.org/10.1007/s11856-022-2323-5 (Access: Geschlossen)