Overconvergent Eichler-Shimura isomorphisms

TL;DR

This paper establishes a geometric Hodge-Tate map that describes overconvergent modular symbols in terms of overconvergent modular forms, advancing the understanding of p-adic modular forms and their associated Galois representations.

Contribution

It introduces a new geometric Hodge-Tate map that links overconvergent modular symbols to overconvergent modular forms in a p-adic setting.

Findings

Provides a generic description of overconvergent modular symbols

Connects modular symbols with overconvergent modular forms of shifted weight

Enhances understanding of p-adic Hodge theory in modular forms

Abstract

We provide a geometric Hodge-Tate map giving generic description of the overconvergent modular symbols of some p-adic (accessible) weight k, base-changed to C_p, in terms of overconvergent modular forms of weight k+2.