$p$-torsion of Jacobians for unramified $\mathbb{Z}/p\mathbb{Z}$-covers of curves

Abstract: It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map $M_g\to A_g$ which sends a curve $X$ to its Jacobian $J_X$. In characteristic $p$, $A_g$ has interesting filtrations, and we can ask how the image of $M_g$ interacts with them. Concretely, which groups schemes arise as the p-torsion subgroup $J_X[p]$ of a Jacobian? We consider this problem in the context of unramified $Z/pZ$ covers $Y\to X$ of curves, asking how $J_Y[p]$ is related to $J_X[p]$. 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.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar