J.Bellaïche and M.Dimitrov have shown that the p-adic eigencurve is smooth but not étale over the weight space at p-regular theta series attached to a character of a real quadratic field F in which p splits.

We study some p-adic properties of modular forms over unitary Shimura curves, including a description of their relation with automorphic representations via p-adic Hodge theory, overconvergence and classicality, and p-adic families.

We consider three Coleman families of modular forms and we would like to construct a p-adic L-function interpolating the algebraic part of central values of the triple product L-function attached to these families and classical weights.