On $p$-adic $L$-functions for Hilbert modular forms

Abstract

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does not require any small slope or non-criticality assumptions on the $p$-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group and a smoothness theorem for certain eigenvarieties at critically refined points.

101 pages. Substantial revision from v1. Results remain the same, but numbering has been altered. Accepted to Memoirs of the AMS

References in corpus (2)

• Deformations of polarized automorphic Galois representations and adjoint Selmer groups
• A local model for the trianguline variety and applications

Cited by in corpus (2)

• Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism
• Iwasawa theory for quadratic Hilbert modular forms