Explicit Vologodsky Integration for Hyperelliptic Curves

Enis Kaya (University of Groningen)

22-Mar-2021, 12:15-13:15 (3 years ago)

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 algorithms for computing these 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.

number theory

Audience: researchers in the topic


Warsaw Number Theory Seminar

Organizers: Jakub Byszewski*, Bartosz Naskręcki, Bidisha Roy, Masha Vlasenko*
*contact for this listing

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