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Iwasawa theory for modular forms at supersingular primes

Part of: Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  07 February 2011

Antonio Lei
Antonio Lei*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (email: antonio.lei@monash.edu)
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Abstract

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We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of the plus and minus Coleman maps for normalised new forms of arbitrary weights and relate Pollack’s p-adic L-functions to the plus and minus Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the ‘main conjecture’ for CM modular forms.

Keywords

modular formsupersingular primeIwasawa theoryCM form

MSC classification

Secondary: 11R23: Iwasawa theory 11F11: Holomorphic modular forms of integral weight

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 3 , May 2011 , pp. 803 - 838
Copyright
Copyright © Foundation Compositio Mathematica 2011

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