Number Theory Seminar
Tian Wang
University of Illinois at Chicago
Distribution problems associated to abelian varieties
Abstract: Given an abelian variety 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