Seminar Algebra and Topology

The seminar usually takes place Wednesdays in I.13.71 (!), 16:30 - 17:30.
Involved professors: Jens Hornbostel, Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth, Matthias Wendt.

 

Christopher Lazda: Boundedness of the p-primary torsion of the Brauer groups of K3 surfaces

The transcendental Brauer group of a variety X over a field k is the image of its Brauer group inside the Brauer group of the base change of X to a separable closure of k. If X is a K3 surface, and k is finitely generated of characteristic 0, then it was shown by Skorobogatov and Zarhin that this group is finite. If k is finitely generated of characteristic p (and X is again a K3 surface), then later work of Skorobogatov and Zarhin (in the case p =/=2) and Ito (in the case p=2) showed that its prime-to-p torsion subgroup is finite. One cannot in general expect finiteness of p-torsion in characteristic p, however, I will explain how to use Madapusi-Pera's proof of the Tate conjecture for K3 surface to show that one does have such a finiteness result in the case that X is non-supersingular. Combined with known results in the supersingular case, this shows that, in general, the p-torsion will always at least be of finite exponent, that is, annihilated by a fixed power of p. This is joint work with Alexei Skorobogatov.

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