Overconvergent cohomology, p-adic L-functions and families for GL(2) over CM fields

Abstract

The study of overconvergent cohomology, initiated by Pollack and Stevens in the setting of classical modular forms, has now been used to construct p-adic L-functions in a number of settings. The method is conceptual and is very closely related to the recent constructions of eigenvarieties by Ash–Stevens, Urban and Hansen. In this note, we give an exposition of the ideas behind the use of overconvergent cohomology in constructing p-adic L-functions, and use it to construct p-adic L-functions attached to base-change families of automorphic representations for GL(2) over CM fields. As a corollary, we prove a p-adic Artin formalism result for base-change p-adic L-functions.