Overconvergent Eichler-Shimura isomorphisms for quaternionic modular forms over Q

In this work, we construct overconvergent Eichler-Shimura isomorphisms over Shimura curves over Q. More precisely, for a prime p > 3 and a wide open disk U in the weight space, we construct a Hecke-Galois-equivariant morphism from the space of families of overconvergent modular symbols over U to the space of families of overconvergent modular forms over U. In addition, for all but finitely many weights.. U, this morphism provides a description of the finite slope part of the space of overconvergent modular symbols of weight. in terms of the finite slope part of the space of overconvergent modular forms of weight lambda+ 2. Moreover, for classical weights these overconvergent isomorphisms are compatible with the classical Eichler-Shimura isomorphism.