The p-torsion of the Brauer group of an abelian variety

Abstract: I will present a new finiteness result for the $p$-primary torsion of the transcendental Brauer group of abelian varieties in characteristic $p$. This follows from a certain “fppf variant” of the Tate conjecture for abelian varieties. The main ingredient in the proof is de Jong's crystalline Tate conjecture. In the talk, I will recall de Jong's theorem, the relation between crystalline cohomology and the fppf cohomology of $\mu_p^n$, and I will explain some steps of the proof.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html