Algebraic Geometry Seminar

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A variety that cannot be dominated by one that lifts

Speaker: Remy van Dobben de Bruyn, Princeton University and Institute for Advanced Study

Location: Warren Weaver Hall 317

Date: Thursday, October 31, 2019, 5 p.m.

Synopsis:

The recent proofs of the Tate conjecture for K3 surfaces over finite fields start by lifting the surface to characteristic 0. Serre showed in the sixties that not every variety can be lifted, but the question whether every motive lifts to characteristic 0 is open. We give a negative answer to a geometric version of this question, by constructing a smooth projective variety that cannot be dominated by a smooth projective variety that lifts to characteristic 0.