Journal article

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

Abstract:

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 som...

### Authors

Publication date:
2012-01-29
URN:
uuid:b0ed144a-7e6d-4f57-a29c-f6fccaac8268
Source identifiers:
398263
Local pid:
pubs:398263
Keywords: