Specializations of quaternionic big Heegner classes

In this thesis, we construct generalized Heegner classes associated to quaternionic modular forms and the big Heegner classes that p-adically interpolate them along a Coleman (finite slope) family of quaternionic modular forms, following the motivic approach introduced by Jetchev--Loeffler--Zerbes. We also describe the specialization of the big Heegner classes in classical weights.