## Lethbridge Number Theory and Combinatorics Seminar: Douglas Ulmer

- Date: 03/27/2023
- Time: 11:00

University of Lethbridge

p-torsion of Jacobians for unramified Z/pZ-covers of curves

It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map Mg→Ag which sends a curve X to its Jacobian JX. In characteristic p, Ag has interesting filtrations, and we can ask how the image of Mg interacts with them. Concretely, which groups schemes arise as the p-torsion subgroup JX[p] of a Jacobian? We consider this problem in the context of unramified Z/pZ covers Y→X of curves, asking how JY[p] is related to JX[p]. Translating this into a problem about de Rham cohmology yields some results using classical ideas of Chevalley and Weil.

This is joint work with Bryden Cais.

**Time**: 11am Pacific/ 12pm Mountain

**Online Via Zoom**:

https://uleth.zoom.us/meeting/register/tJcpc--rjwsGtE7inVJcDzcjleYhbzaso14