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The adic, cuspidal, Hilbert eigenvarieties. (English) Zbl 1417.11063
Summary: We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral families of modular sheaves on the relevant formal Shimura schemes.

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
Full Text: DOI
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