Anticyclotomic Iwasawa%26apos;s Main Conjecture for Hilbert modular forms

作者：Longo Matteo^*

来源：Commentarii Mathematici Helvetici, 2012, 87(2): 303-353.

DOI：10.4171/CMH/255

• Hilbert modular forms
• Iwasawa theory

Let F/Q be a totally real extension and f an Hilbert modular cusp form of level it, with trivial central character and parallel weight 2, which is an eigenform for the action of the Hecke algebra. Fix a prime p vertical bar n of F of residual characteristic p. Let K/F be a quadratic totally imaginary extension and K-p infinity be the p-anticyclotomic Z(p)-extension of K. The main result of this paper, generalizing the analogous result [5] 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 to (f, K-p infinity) divides the p-adic L-function attached to (f, Kp(infinity)), thus proving one direction of the Anticyclotomic Main Conjecture for Hilbert modular forms. Arithmetic applications are given.

• 出版日期2012