AAG Seminar: Vertical Frobenius distributions for abelian varieties over finite fields

Speaker: Soumya Sankar, Utrecht University

Abstract: Elliptic curves over a finite field F_q come in two flavours: ordinary and supersingular. As q varies over powers of a fixed prime p, the eigenvalues of Frobenius of an ordinary elliptic curve are uniformly distributed on a circle, while those of a supersingular elliptic curve are supported are finitely many places. In joint work with Santiago Arango-Piñeros and Deewang Bhamidipati, we study this phenomenon for abelian varieties in higher dimensions, and provide a classification of the possible scenarios in low dimension. In this talk, I will discuss some of our results and some open questions in this area.

Host: Wanlin Li