Explicit Vologodsky Integration for Hyperelliptic Curves

Abstract: Let $X$ be a curve over a $p$-adic field with semi-stable reduction and let $\omega$ be a meromorphic $1$-form on $X$. There are two notions of p-adic integration one may associate to this data: the Berkovich–Coleman integral which can be performed locally; and the Vologodsky integral with desirable number-theoretic properties. In this talk, we present a theorem comparing the two, and describe an algorithm for computing Vologodsky integrals in the case that $X$ is a hyperelliptic curve. We also illustrate our algorithm with a numerical example computed in Sage. This talk is partly based on joint work with Eric Katz.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.