Open AccessAnticyclotomic Iwasawa’s Main Conjecture for Hilbert modular forms
Author(s) -
Matteo Longo
Publication year - 2012
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.4171/cmh/255
Subject(s) - mathematics , modular form , conjecture , cusp (singularity) , iwasawa theory , pure mathematics , prime (order theory) , cusp form , algebra over a field , holomorphic function , modular group , combinatorics , geometry
Let F be a totally real extension and f an Hilbert modular cusp form of level n, with trivial central character and parallel weight 2, which is an eigenform for the action of the Heckealgebra. Fix a prime P of F of residual characteristic p. Let K be a quadratic totally imaginary extension of F and K' be the P-anticyclotomic Zp-extension of K. The main resultof this paper, generalizing the analogous result of Bertolini and Darmon, states that, under suitable arithmetic assumptions and some technical restrictions, the characteristic power series of the Pontryagin dual of the Selmer group attached of f over K' divides the p-adic L-function attached to f and K' thus proving one direction of the Anticyclotomic Main Conjecture for Hilbert modular forms. Arithmetic applications are given