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On overconvergent Hilbert modular cusp forms. (À propos des formes modulaires surconvergentes cuspidales de Hilbert.) (English. French summary) Zbl 1408.11037

Andreatta, Fabrizio et al., Arithmétique \(p\)-adique des formes de Hilbert. Paris: Société Mathématique de France (SMF). Astérisque 382, 163-193 (2016).
Summary: We \(p\)-adically interpolate modular invertible sheaves over a strict neighborhood of the ordinary locus of a Hilbert modular variety. We then prove the existence of finite slopes families of cuspidal eigenforms.
For the entire collection see [Zbl 1353.11003].

MSC:

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F85 \(p\)-adic theory, local fields
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