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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.

MSC:
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)
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