Finiteness of K3 surfaces and the Tate conjecture

Published 6 Jul 2011 in math.AG and math.NT | (1107.1221v5)

Abstract: Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only finitely many K3 surfaces over each finite extension of k.

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