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Derived p-adic heights and p-adic L-functions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 126, Number 6, December 2004
- pp. 1315-1340
- 10.1353/ajm.2004.0045
- Article
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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 Zp-extension to be "semi-simple" as an Iwasawa module, generalizing results of Perrin-Riou.