Overconvergent Eichler-Shimura Isomorphisms for Unitary Shimura Curves over Totally Real Fields

We compare two different cohomology groups on unitary Shimura curves over totally real number fields; these groups are used in the construction of p-adic families of modular forms in this context. More precisely, we describe the space of finite slope overconvergent modular forms of any weight in terms of a convenient overconvergent cohomology. © 2021, The Hebrew University of Jerusalem.