Triple product p -adic L -functions for Shimura curves over totally real number fields

Let F be a totally real number field. Using a recent geometric approach developed by Andreatta and Iovita we construct several variables p -adic families of finite slope quaternionic automorphic forms over F . It is achieved by interpolating the modular sheaves defined over some auxiliary unitary Shimura curves. Secondly, we attach p -adic L -functions to triples of ordinary p -adic families of quaternionic automorphic eigenforms. This is done by relating trilinear periods to some trilinear products over unitary Shimura curves which can be interpolated adapting the work of Liu–Zhang–Zhang to our families.