EVENT DETAILS AND ABSTRACT

Title: Overconvergent Eichler–Shimura morphism for families of Siegel modular forms
Speaker: Giovanni Rosso
Speaker Info: Concordia University
Brief Description:
Special Note:
Abstract:

Classical results of Eichler and Shimura decompose the cohomology of certain local systems on the modular curve in terms of holomorphic and anti-holomorphic modular forms. A similar result has been proved by Faltings for the etale cohomology of the modular curve and Faltings' result has been partly generalised to Coleman families by Andreatta–Iovita–Stevens. In this talk, based on joint work with Hansheng Diao and Ju-Feng Wu, I will explain how one constructs a morphism from the overconvergent cohomology of GSp_2g to the space of families of Siegel modular forms. This can be seen as a first step in an Eichler--Shimura decomposition for overconvergent cohomology and involves a new definition of the sheaf of overconvergent Siegel modular forms using the Hodge–Tate map at infinite level. If time allows it, I'll explain how one can hope to use higher Coleman theory to find a complete analogue of the classical Eichler–Shimura decomposition in small slope.