François Charles, Zarhin's trick for K3 surfaces and the Tate conjecture

Zarhin's trick for K3 surfaces and the Tate conjecture If A is an abelian variety over an arbitrary field, Zarhin's trick shows that (AxA)^4 can be endowed with a principal polarization. Using moduli spaces of stable sheaves, we prove a general version of Zarhin's trick for K3 surfaces over arbitrary fields. As an application, we will give a simple proof of the Tate conjecture for K3 surfaces over arbitrary finite fields.