Computing local p-adic height pairings on hyperelliptic curves

2010/10/28 by Balakrishnan, Jennifer S., Besser, Amnon
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1010.6009

Abstract

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.

Related

• Computing p-adic heights on hyperelliptic curves
• Explicit Coleman integration for hyperelliptic curves
• The p-adic height pairings of Coleman-Gross and of Nekovar
• Coleman-Gross height pairings and the p-adic sigma function
• Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves