Compositio Mathematica

Iwasawa Theory for Elliptic Curves at Unstable Primes

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

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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.

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