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

John Bergdall; David Hansen

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

Number Theory 2022-02-10 v2

Authors: John Bergdall , David Hansen

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.

Keywords

p-adic analysis p-adic hodge theory holomorphic mappings

Cite

@article{arxiv.1710.05324,
  title  = {On $p$-adic $L$-functions for Hilbert modular forms},
  author = {John Bergdall and David Hansen},
  journal= {arXiv preprint arXiv:1710.05324},
  year   = {2022}
}

Comments

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

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

Abstract

Keywords

Cite

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