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Thursday 17 Feb 2022Pure Mathematics Seminar: Good reduction of Kummer surfaces modulo 2

Dr Chris Lazda - University of Exeter

Harrison 203 14:30-15:30

Kummer surfaces form a particular class of K3 surfaces arising from abelian surfaces. In residue characteristic different from 2, their good reduction is essentially equivalent to the good reduction of the initial abelian surface, and is therefore completely understood via the classical Neron—Ogg—Shafarevich criterion. In residue characteristic 2, however, things are a little bit more interesting, and good reduction of the initial abelian surface is not enough to ensure good reduction of the associated Kummer. In this talk I will explain a more refined criterion for the good reduction of K3 surfaces, and use it to solve the problem of good reduction for Kummer surfaces associated to abelian surfaces with good, non-supersingular reduction in residue characteristic 2. This is joint work with Evis Ieronymou and Alexei Skorobogatov.

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