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

John Bergdall; David Hansen

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arXiv · 1710.05324

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

John Bergdall·David Hansen

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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.

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John Bergdall, David Hansen. 2021-12-21. On $p$-adic $L$-functions for Hilbert modular forms. https://arxiv.org/abs/1710.05324

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