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 λ ∈ U , this morphism provides a description of the finite slope part of the space of overconvergent modular symbols of weight λ in terms of the finite slope part of the space of overconvergent modular forms of weight λ + 2. Moreover, for classical weights these overconvergent isomorphisms are compatible with the classical Eichler-Shimura isomorphism