Iwasawa Theory for Modular Forms at Supersingular Primes
Number Theory
2011-06-09 v3
Abstract
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 even and odd Coleman maps for normalised new forms of arbitrary weights and relate Pollack's -adic -functions to the even and odd Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the "main conjecture" for CM modular forms.
Cite
@article{arxiv.0904.3938,
title = {Iwasawa Theory for Modular Forms at Supersingular Primes},
author = {Antonio Lei},
journal= {arXiv preprint arXiv:0904.3938},
year = {2011}
}
Comments
Has been expanded and revised incorporating comments made by the referees. To appear in Compositio Mathematica