Vologodsky integration on curves with semi-stable reduction

Amnon Besser, Sarah Livia Zerbes

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove that the Vologodsky integral of a meromorphic one-form on a curve over a p-adic field with semi-stable reduction restrict to Coleman integrals on the rigid subdomains reducing to the components of the smooth part of the special fiber and that on the connecting annuli the differences of these Coleman integrals form a harmonic cochain on the edges of the dual graph of the special fiber. This determines the Vologodsky integral completely. We analyze the behavior of the integral on the connecting annuli and we explain the results in the case of a Tate elliptic curve.

Original languageEnglish
Pages (from-to)761-770
Number of pages10
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - 1 Mar 2023

ASJC Scopus subject areas

  • General Mathematics


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