Derived categories of K3 surfaces in positive characteristic

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• Max Lieblich (Washington)
• Wednesday 04 May 2011, 14:30-15:30
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

Mukai proved that the derived category of a K3 surface over the complex numbers is governed by a Torelli-like theorem for a Hodge structure of weight 2 on its total cohomology. As a consequence of this and the classical Torelli theorem, one can describe all of the K3 surfaces with a given derived category and show that there are in fact only finitely many. I will describe what can be proven in characteristic p. In particular, I will explain why there are only finitely many K3 surfaces with a given derived category. This is a report on joint work in progress with Martin Olsson.

This talk is part of the Algebraic Geometry Seminar series.

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