Compositio Mathematica



Iwasawa Theory for Elliptic Curves at Unstable Primes


DANIEL DELBOURGO a1
a1 University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England.

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Abstract

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.


Key Words: p-adic L-functions; Iwasawa theory; modular forms; elliptic curves..