Adrian Iovita (Concordia University)
An overconvergent crystalline Eichler-Shimura isomorphism

Abstract: The classical Eichler-Shimura isomorphism is an isomorphism which describes the Hecke module of weight k modular symbols (k a non-negative integer) in terms of the relevant modular forms of weight k+2. We now fix a prime p>2. An overconvergent, p-adic, crystalline Eichler-Shimura isomorphism would then be an isomorphism describing (a part of) the crystalline Fontaine module associated to the overconvergent modular symbols of weight k (this time k is a p-adic weight), as a Hecke module, in terms of finite slope overconvergent modular forms of weight k+2. Recently, with Fabrizio Andreatta we have constructed such an isomorphism.