Tian Wang : On the distribution of supersingular primes of abelian surfaces

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

March 8, 2024, 1 p.m.

In

427 SEO

Abstract

Let $ E$ over $\bf{Q}$ be an elliptic curve without complex multiplication. Lang and Trotter made a conjecture regarding the number of primes $p$ up to $x$ for which the reduction of $E$ at $p$ is supersingular. Though the conjecture is still open, we now have unconditional upper and lower bounds, thanks to the work of several mathematicians in the past few decades. However, much less has been studied for the distribution of supersingular primes for abelian surfaces (even conjecturally). In this talk, I will present my recent work on unconditional upper bounds for the number of primes $p$ up to $x$ for which the reduction of a fixed abelian surface at $p$ is supersingular.