Simple abelian varieties over finite fields with extreme point counts

Abstract: Given a compactly supported probability measure on the reals, we will give a necessary and sufficient condition for there to be a sequence of totally real algebraic integers whose distribution of conjugates approaches the measure. We use this result to prove that there are infinitely many totally positive algebraic integers X satisfying tr(X)/deg(X) < 1.899; previously, there were only known to be infinitely many such integers satisfying tr(X)/deg(X) < 2. We also will explain how our method can be used in the search for simple abelian varieties with extreme point counts.

number theory

Audience: researchers in the topic

BC-MIT number theory seminar