Taylor Dupuy (Nov. 13, 2020): Abelian Varieties Over Finite Fields in the LMFDB
Channel: Algebraic Geometry at Stanford
Date: 2021-03-07

I will talk about things around the LMFDB database of isogeny classes of abelian varieties over finite fields (and maybe even about isomorphism classes). 

These could include: 
--"Sato-Ain't" distributions, 
--weird Tate classes, 
--Bizzaro Hodge co-levels (and very strange Ax-Katz/Chevalley-Warning type congruences with fractional exponent!), 
--the counter-example to the conjecture of Ahmadi-Shparlinski,
--what we know about angle ranks vs galois groups vs Newton polygons,
--new conjectures 

The database and "census" is joint work with Kiran Kedlaya, David Roe, and Christelle Vincent (currently available on the arxiv). The work on Tate classes is ongoing with Kiran Kedlaya and David Zureick-Brown.