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- Title
Boundedness of the p -primary torsion of the Brauer group of an abelian variety.
- Authors
D'Addezio, Marco
- Abstract
We prove that the $p^\infty$ -torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for abelian varieties. To do this, we prove a 'flat Tate conjecture' for divisors. We also study other geometric Galois-invariant $p^\infty$ -torsion classes of the Brauer group which are not in the transcendental Brauer group. These classes, in contrast with our main theorem, can be infinitely $p$ -divisible. We explain how the existence of these $p$ -divisible towers is naturally related to the failure of surjectivity of specialisation morphisms of Néron–Severi groups in characteristic $p$.
- Subjects
BRAUER groups; ABELIAN groups; TORSION; ABELIAN varieties; SURJECTIONS; DIVISIBILITY groups; TORSION theory (Algebra)
- Publication
Compositio Mathematica, 2024, Vol 160, Issue 2, p463
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X23007558