Jaclyn Lang

The Hodge and Tate Conjectures for self-products of K3 surfaces with non-symplectic group actions

There are 16 K3 surfaces (defined over \mathbb{Q}) that Livné-Schütt-Yui have shown are modular, in the sense that the transcendental part of their cohomology is given by an algebraic Hecke character. Using this modularity result, we show that for any of these K3 surfaces X, the variety X^n satisfies the Hodge and Tate Conjectures for any positive integer n. If time permits, we will explain how our methods can also be applied to a certain family of curves. This is joint work in progress with Laure Flapan.