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

Ben-Gurion University of the Negev

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

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	American 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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1093/imrn/rnr111

Cite this

@article{c1bcc0c6276c41b4bcd02dc3d1cd8b29,

title = "Computing local p-adic height pairings on hyperelliptic curves",

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.",

year = "2012",

month = jun,

day = "11",

doi = "10.1093/imrn/rnr111",

language = "American English",

volume = "2012",

pages = "2405--2444",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "11",

}

TY - JOUR

T1 - Computing local p-adic height pairings on hyperelliptic curves

AU - Balakrishnan, Jennifer S.

AU - Besser, Amnon

N1 - 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.

PY - 2012/6/11

Y1 - 2012/6/11

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.

UR - http://www.scopus.com/inward/record.url?scp=84861893802&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnr111

DO - 10.1093/imrn/rnr111

M3 - Article

SN - 1073-7928

VL - 2012

SP - 2405

EP - 2444

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 11

ER -

Computing local p-adic height pairings on hyperelliptic curves

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this