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THE ANTICYCLOTOMIC MAIN CONJECTURE FOR ELLIPTIC CURVES AT SUPERSINGULAR PRIMES

Published online by Cambridge University Press:  16 November 2007

Henri Darmon  and
Adrian Iovita
Henri Darmon
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street, West Montreal, Quebec H3A 2K6, Canada ([email protected])
Adrian Iovita
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard, West Montreal, Quebec H3G 1M8, Canada ([email protected])
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Abstract

The Main Conjecture of Iwasawa theory for an elliptic curve $E$ over $\mathbb{Q}$ and the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K$ was studied in \cite{bertolini_darmon}, in the case where $p$ is a prime of ordinary reduction for $E$. Analogous results are formulated, and proved, in the case where $p$ is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, Pollack, Kurihara, Kobayashi and Iovita and Pollack are required to handle this case in which many of the simplifying features of the ordinary setting break down.

Keywords

elliptic curvessupersingular reductionIwasawa theoryMain Conjecture$p$-adic $L$-functionsPrimary 11R2311G05
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 2 , April 2008 , pp. 291 - 325
Copyright
2007 Cambridge University Press

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