1. DERIVED P-ADIC HEIGHTS AND P-ADIC L-FUNCTIONS.
- Author
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Howard, Benjamin
- Subjects
- *
ELLIPTIC curves , *MATHEMATICAL functions , *P-adic groups , *COMPLEX numbers , *DIFFERENTIAL equations , *MATHEMATICS - Abstract
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 F over a Zp-extension to be "semi-simple" as an Iwasawa module, generalizing results of Perrin-Riou. [ABSTRACT FROM AUTHOR]
- Published
- 2004
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