Derived p-adic heights and p-adic L-functions

Details Derived p-adic heights and p-adic L-functions Derived p-adic heights and p-adic L-functions

2012-02-28

arxiv.org/abs/1202.6343v1

Amer. J. Math. 126, No. 6 (2004), 1315-1340

Mathematics

Number Theory

Scientific paper

If E is an elliptic curve defined over a number field and p is a prime of good ordinary reduction for E, a theorem of Rubin relates the p-adic height pairing on the p-power Selmer group of E to the first derivative of a cohomologically defined p-adic L-function attached to E. Bertolini and Darmon have defined a sequence of "derived" p-adic heights. In this paper we give an alternative definition of the p-adic height pairing and prove a generalization of Rubin's result, relating the derived heights to higher derivatives of p-adic L-functions. We also relate degeneracies in the derived heights to the failure of the Selmer group of E over a Z_p-extension to be "semi-simple" as an Iwasawa module, generalizing results of Perrin-Riou.

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