Abstract

A class result of Deuring expresses a relation between the number of supersingular elliptic curves and the number of their endomorphism rings and those which are defined over Fp. Deuring's result was generalized to polarized supespecial abelian varieties by Ibukiyama and Katsura. In this talk we shall explore finer classification for polarized superspecial abelian varieties over Fp up to isomorphism over Fp rather than its algebraic closure. A key tool is the lattice description of polarized abelian varieties over Fp isogenous to a power of elliptic curves. This is joint work with Yuchui Lin and Jiangwei Xue.  

 

Organizer: Chia-Fu Yu (AS)