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Vologodsky integration on curves with semi-stable reduction

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Abstract

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.

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Author notes

  1. Sarah Livia Zerbes

    Present address: ETH Zürich, Rämistrasse 101, 8003, Zürich, Switzerland

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev Be’er Sheva, Be’er Sheva, 84105, Israel

    Amnon Besser

  2. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK

    Sarah Livia Zerbes

Authors
  1. Amnon Besser
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  2. Sarah Livia Zerbes
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Correspondence to Amnon Besser.

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Besser, A., Zerbes, S.L. Vologodsky integration on curves with semi-stable reduction. Isr. J. Math. 253, 761–770 (2023). https://doi.org/10.1007/s11856-022-2377-4

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  • DOI: https://doi.org/10.1007/s11856-022-2377-4

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