Computing local p-adic height pairings on hyperelliptic curves

Journal article

We describe an algorithm to compute the local component at p of the Coleman-Gross p-adic height pairing on 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.

Authors: Balakrishnan, J; Besser, A

• Journal: International Mathematics Research Notices
• Volume: 2012
• Issue: 11
• Pages: 2405-2444
• Publication date: 2010-10-28
• DOI: 10.1093/imrn/rnr111
• EISSN: 1687-0247
• ISSN: 1073-7928
• Language: English
• Keywords: math.NT; math.AG