Title: Counting abelian varieties over finite fields.
Speaker: 薛江维（武汉大学）
Time: 1.23 (Friday), 09:30-10:30
Venue: Room 315, Gewu Building
Abstract: In this talk we explain an elementary method for counting abelian varieties equipped with PEL-type structures. Analogous to the study of (quadratic/hermitian) lattices over orders, the abelian varieties within an isogeny class are classified into genera according to their local isomorphism classes. The number of isomoprhism classes within each genus is then shown to be equal to the class number of a suitable algebraic group. We apply this strategy to several counting problems of superspecial abelian varieties over finite fields. This talk is based on joint works with Yasuhiro Terakado and Chia-Fu Yu.
