The Hodge and Tate Conjectures for self-products of two K3 surfaces

par Jaclyn Lang (Paris 13)

jeudi 7 nov. 2019, 14:00 → 15:00 Europe/Paris

Salle M7 (UMPA, ENS de Lyon)

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 two of these K3 surfaces X, the variety X^n satisfies the Hodge and Tate Conjectures for any positive integer n.  In the talk, we will discuss the details of the Tate Conjecture for X^2. This is joint work in progress with Laure Flapan.