Iwasawa Theory for Modular Forms at Supersingular Primes

Details Iwasawa Theory for Modular Forms at Supersingular Primes Iwasawa Theory for Modular Forms at Supersingular Primes

2009-04-24

arxiv.org/abs/0904.3938v3

Compos. Math. 147 (2011), no.3, 803-838

Mathematics

Number Theory

Has been expanded and revised incorporating comments made by the referees. To appear in Compositio Mathematica

Scientific paper

10.1112/S0010437X10005130

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 $p$-adic $L$-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.

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