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

Speaker: Douglas Ulmer

Date: Mon, Mar 27, 2023

Location: Online, PIMS, University of Lethbridge

Conference: Lethbridge Number Theory and Combinatorics Seminar

Subject: Mathematics

Class: Scientific


Douglas Ulmer (University of Arizona, USA)

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.

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