p-adic heights and Vologodsky integration

Amnon Besser

doi:10.1016/j.jnt.2021.12.005

p-adic heights and Vologodsky integration

Amnon Besser

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We extend the result of [5] to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a p-adic height pairing. We show that this pairing still equals the one defined by Nekovář.

Original language	English
Pages (from-to)	273-297
Number of pages	25
Journal	Journal of Number Theory
Volume	239
DOIs	https://doi.org/10.1016/j.jnt.2021.12.005
State	Published - 1 Oct 2022

Keywords

Coleman integration
p-adic height pairings
Semi stable reduction
Vologodsky integration

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2021.12.005

Cite this

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title = "p-adic heights and Vologodsky integration",

abstract = "We extend the result of [5] to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a p-adic height pairing. We show that this pairing still equals the one defined by Nekov{\'a}{\v r}.",

keywords = "Coleman integration, p-adic height pairings, Semi stable reduction, Vologodsky integration",

author = "Amnon Besser",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

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day = "1",

doi = "10.1016/j.jnt.2021.12.005",

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AU - Besser, Amnon

PY - 2022/10/1

Y1 - 2022/10/1

N2 - We extend the result of [5] to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a p-adic height pairing. We show that this pairing still equals the one defined by Nekovář.

AB - We extend the result of [5] to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a p-adic height pairing. We show that this pairing still equals the one defined by Nekovář.

KW - Coleman integration

KW - p-adic height pairings

KW - Semi stable reduction

KW - Vologodsky integration

UR - http://www.scopus.com/inward/record.url?scp=85124197683&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2021.12.005

DO - 10.1016/j.jnt.2021.12.005

M3 - Article

AN - SCOPUS:85124197683

SN - 0022-314X

VL - 239

SP - 273

EP - 297

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

p-adic heights and Vologodsky integration

Abstract

Keywords

ASJC Scopus subject areas

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