Iwasawa theory for modular forms at supersingular primes

作者：Lei Antonio^*

来源：Compositio Mathematica, 2011, 147(3): 803-838.

DOI：10.1112/S0010437X10005130

• modular form
• supersingular prime
• Iwasawa theory
• CM form

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.

• 出版日期2011-5