On the anticyclotomic Iwasawa's main conjecture for Hilbert modular forms

This paper generalizes to the totally real case the previous work of Bertolini and Darmon on the Anticyclotomic Iwasawa's Main Conjecture for modular forms over Q with coefficients in Z_p. It contains the definition of anticyclotomic p-adic L-functions attached to Hilbert modular forms and the generalization of the main result of Bertolini and Darmon to this context. The main feature of the totally real case is the possibility of defining several p-adic L functions (each in several variables) corresponding to different divisors of p: the paper also explores the relations between these different functions.