Number Theory Seminar
Tian Wang
Max Planck Institute for Mathematics, Bonn, Germany
On the distribution of supersingular primes of abelian surfaces
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.
Friday March 8, 2024 at 1:00 PM in 427 SEO