Computing local $p$-adic height pairings on hyperelliptic curves Academic Article uri icon

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.

publication date

  • January 1, 2012