Coleman-Gross height pairings and the p-adic sigma function

Jennifer S. Balakrishnan, Amnon Besser

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We give a direct proof that the Mazur-Tate and Coleman-Gross heights on elliptic curves coincide. The main ingredient is to extend the Coleman-Gross height to the case of divisors with non-disjoint support and, doing some p-adic analysis, show that, in particular, its component above p gives, in the special case of an ordinary elliptic curve, the p-adic sigma function. We use this result to give a short proof of a theorem of Kim characterizing integral points on elliptic curves in some cases under weaker assumptions. As a further application, we give new formulas to compute double Coleman integrals from tangential basepoints.

Original languageEnglish
Pages (from-to)89-104
Number of pages16
JournalJournal fur die Reine und Angewandte Mathematik
Issue number698
StatePublished - 1 Jan 2015

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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