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Iwasawa Theory for Elliptic Curves at Unstable Primes

Published online by Cambridge University Press:  04 December 2007

DANIEL DELBOURGO
DANIEL DELBOURGO
Affiliation:
University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England.
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Abstract

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In this paper we examine the Iwasawa theory of modular elliptic curves E defined over Q without semi-stable reduction at p. By constructing p-adic L-functions at primes of additive reduction, we formulate a “Main Conjecture” linking this L-function with a certain Selmer group for E over the Zp-extension. Thus the leading term is expressible in terms of III$_E$, E(Q)$_tors$ and a p-adic regulator term.

Keywords

p-adic L-functionsIwasawa theorymodular formselliptic curves.
Type
Research Article
Information
Compositio Mathematica , Volume 113 , Issue 2 , September 1998 , pp. 123 - 154
Copyright
© 1998 Kluwer Academic Publishers