A generalization of Elkies’ theorem on infinitely many supersingular primes

Abstract: In 1987, Elkies proved that every elliptic curve defined over $\mathbb{Q}$ has infinitely many supersingular primes. In this talk, I will present an extension of this result to certain abelian fourfolds in Mumford’s families and more generally, to some Kuga-Satake abelian varieties constructed from K3-type Hodge structures with real multiplication. I will review Elkies’ proof and explain how his strategy of intersecting with CM cycles can be adapted to our setting. I will also discuss some of the techniques in our proof to study the local properties of the CM cycles.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper )

Boston University Number Theory Seminar