Finiteness of K3 surfaces and the Tate conjecture

Details Finiteness of K3 surfaces and the Tate conjecture Finiteness of K3 surfaces and the Tate conjecture

2011-07-06

arxiv.org/abs/1107.1221v3

Mathematics

Algebraic Geometry

18 pages, even more revised version: dependency on Nygaard-Ogus removed, field extension needed to Tate and finiteness radical

Scientific paper

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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