Abelian Varieties Multi-Site Seminar Series: Andrew Fiori

Let K be a quadratic imaginary field, and p be a prime which is inert in K. It is known that the mod p reductions of the j-invariants of elliptic curves defined over the algebraic closure of Q_p which admit CM by an order of K are equidistributed among the supersingular values in F_{p²}. By contrast, if we replace this algebraically closed field by Q_p, the j-invariants for many natural families of orders do not share this same distribution and are simply not uniformly distributed among all the supersingular values in F_p.

In this talk I will explain why this occurs, and some of the computations which led me to consider this question.