From Merel's theorem to Brauer groups of K3 surfaces

Abstract: Over number fields, the Brauer group of a K3 surface behaves similarly to the subgroup of points of finite order of an elliptic curve. In 1996, Merel showed that the order of the torsion subgroup of an elliptic curve E/K is bounded by a constant depending only on the degree of the extension [K:Q]. I will discuss an analogous conjecture in the context of Brauer groups of K3 surfaces, and the evidence we have accumulated so far for it.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic