Computing local p-adic height pairings on hyperelliptic curves

Jennifer S. Balakrishnan; Amnon Besser

doi:10.1093/imrn/rnr111

Computing local p-adic height pairings on hyperelliptic curves

Jennifer S. Balakrishnan, Amnon Besser

Department of Mathematics

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

12 Scopus citations

Abstract

We describe an algorithm to compute the local component, at a prime above the prime p, of the Coleman-Gross p-adic height pairing on degree 0 divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to evaluate Coleman integrals of meromorphic differentials and present our algorithms as implemented in Sage.

Original language	English
Pages (from-to)	2405-2444
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2012
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnr111
State	Published - 11 Jun 2012

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnr111

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abstract = "We describe an algorithm to compute the local component, at a prime above the prime p, of the Coleman-Gross p-adic height pairing on degree 0 divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to evaluate Coleman integrals of meromorphic differentials and present our algorithms as implemented in Sage.",

author = "Balakrishnan, {Jennifer S.} and Amnon Besser",

note = "Funding Information: J.B. was supported by the National Defense Science and Engineering Graduate Fellowship and National Science Foundation Graduate Fellowship. A.B. was supported by the Bell Companies Fellowship and the James D. Wolfensohn fund while at the Institute for Advanced Study and is presently supported by a grant from the Israel Science Foundation.",

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AU - Besser, Amnon

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PY - 2012/6/11

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N2 - We describe an algorithm to compute the local component, at a prime above the prime p, of the Coleman-Gross p-adic height pairing on degree 0 divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to evaluate Coleman integrals of meromorphic differentials and present our algorithms as implemented in Sage.

AB - We describe an algorithm to compute the local component, at a prime above the prime p, of the Coleman-Gross p-adic height pairing on degree 0 divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to evaluate Coleman integrals of meromorphic differentials and present our algorithms as implemented in Sage.

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Computing local p-adic height pairings on hyperelliptic curves

Abstract

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