TY - JOUR

T1 - Coleman-Gross height pairings and the p-adic sigma function

AU - Balakrishnan, Jennifer S.

AU - Besser, Amnon

N1 - Publisher Copyright:
© De Gruyter 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84920964692&partnerID=8YFLogxK

U2 - 10.1515/crelle-2012-0095

DO - 10.1515/crelle-2012-0095

M3 - Article

AN - SCOPUS:84920964692

SN - 0075-4102

SP - 89

EP - 104

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 698

ER -