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arXiv · 1801.07322

A remark on uniform boundedness for Brauer groups

Anna Cadoret·François Charles
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Abstract

The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of $\ell$-primary torsion in the Brauer group. We show that this finiteness is actually uniform in one-dimensional families for varieties that satisfy the Tate conjecture for divisors -- e.g. abelian varieties and $K3$ surfaces.

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Anna Cadoret, François Charles. 2018-01-22. A remark on uniform boundedness for Brauer groups. https://arxiv.org/abs/1801.07322

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