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Algebra Seminar

Friday, October 4, 2019 - 3:15pm

Remy van Dobben de Bruyn

Princeton University and IAS


University of Pennsylvania

4N30 DRL

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.