Algebraic and Arithmetic Geometry Seminar: "Exceptional jumps of the Picard rank of K3 surfaces over number fields"

Speaker: Salim Tayou, Harvard University

Abstract: Given a K3 surface X over a number field K, we prove that the set of primes of K where the geometric Picard rank jumps is infinite. This result is formulated in the general framework of GSpin Shimura varieties and I will explain other applications to abelian surfaces. I will also discuss applications to the existence of rational curves on K3 surfaces.

The results in this talk are partly joint work with Ananth Shankar, Arul Shankar and Yunqing Tang.

Host: Matt Kerr