6 Aprile, 2016 17:00

Seminario Matematico e Fisico di Milano

On the Tate and Mumford-Tate conjectures for varieties with h^{2,0}=1

Ben Moonen, Universita'di Nijmegen

Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50

I will explain my proof of the Tate and Mumford-Tate conjecture for divisor classes on a variety with h^{2,0}=1 (e.g., surfaces with p_g=1), under a mild assumption on their moduli. The proof involves a combination of several new techniques, including a generalization of the Kuga-Satake construction and a new interpretation of 'half-twists' of CM-Hodge structures. I will start by explaining the method of Deligne-Andre for K3 surfaces, which is the main source of inspiration for the proof.