Existence of CM lifts for points on Shimura varieties

Abstract: I'll explain a very simple proof of the fact that K3 surfaces of finite height admit (many) CM lifts, a result due independently to Ito-Ito-Koshikawa and Z. Yang, which was used by the former to prove the Tate conjecture for products of K3s. This will be done directly showing that the deformation ring of a polarized K3 surface of finite height admits as a quotient that of its Brauer group. The method applies more generally to many isogeny classes of points on Shimura varieties of abelian type.

number theory

Audience: researchers in the topic

Harvard number theory seminar