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Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction

Published online by Cambridge University Press:  29 October 2012

CHERN–YANG LEE
CHERN–YANG LEE*
Affiliation:
The School of Mathematical Sciences, The University of Nottingham, Nottingham NG7 2RD. e-mail: chern-yang.lee@nottingham.ac.uk
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Abstract

This paper studies the compact p∞-Selmer Iwasawa module X(E/F∞) of an elliptic curve E over a False Tate curve extension F∞, where E is defined over ℚ, having multiplicative reduction at the odd prime p. We investigate the p∞-Selmer rank of E over intermediate fields and give the best lower bound of its growth under certain parity assumption on X(E/F∞), assuming this Iwasawa module satisfies the H(G)-Conjecture proposed by Coates–Fukaya–Kato–Sujatha–Venjakob.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 303 - 324
Copyright
Copyright © Cambridge Philosophical Society 2012

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