Overconvergent cohomology of Hilbert modular varieties and p-adic L-functions

Abstract

For each Hilbert modular form of non-critical slope we construct a p-adic distribution on the Galois group of the maximal abelian extension unramified outside p and ∞ of the totally real field. We prove that the distribution is admissible and interpolates the critical values of the complex L-function of the form. This construction is based on the study of the overconvergent cohomology of Hilbert modular varieties and certain cycles on these varieties.