Number Theory Seminar 27.05.2024

Speaker: Doug Ulmer (Arizona)

Title: p-torsion of Jacobians in Artin-Schreier covers

Abstract: It is a classical problem to understand the locus of Jacobians of curves in the moduli space of abelian varieties.  In characteristic $p$, the moduli space of abelian varieties has interesting filtrations, and we can ask how the locus of Jacobians interacts with them.  Concretely, which group schemes arise as the p-torsion subgroup of a Jacobian? We consider this problem in the context of unramified Galois covers of curves with group $\mathbb{Z}/p\mathbb{Z}$.  Classical ideas of Chevalley and Weil put strong restrictions on the group scheme "upstairs" and its relationship to the group scheme "downstairs".  This is joint work with Bryden Cais.