Number Theory Seminar
Tian Wang
University of Illinois at Chicago
Distribution problems associated to abelian varieties
Abstract: Given an abelian variety $A$ defined over $\mathbb{Q}$,
we look at its reduction $A_p$ at an arbitrary prime $p$
and study the distribution of $A_p$ with specific properties.
For example, the Lang-Trotter Conjecture about
an abelian variety $A$ of dimension $1$
and its generalizations
to an abelian variety $A$ of higher dimension concern
the distribution of $A_p$ having a prescribed Frobenius trace, while
the Murty-Patankar Conjecture about an absolutely simple abelian variety
$A$
concerns the distribution of $A_p$ having split reduction.
In this talk, I will discuss new upper bounds for
the counting functions related to the aforementioned conjectures.
Friday March 31, 2023 at 12:00 PM in 612 SEO