Number Theory Seminar

Speaker: Salim Tayou (ENS-Paris).

Title: Exceptional jumps of Picard rank for K3 surfaces over number fields.

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, assuming that X has everywhere potentially good reduction. This result is formulated in the general framework of GSpin Shimura varieties and I will explain other applications to abelian surfaces. As a corollary, this gives a new proof that such X has infinitely many rational curves. The results in this talk are joint work with Ananth Shankar, Arul Shankar and Yunqing Tang.

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