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Bijakowski, Stéphane; Pilloni, Vincent; Stroh, Benoît

Classicity of overconvergent modular forms. (Classicité de formes modulaires surconvergentes.) (English. French summary) Zbl 1407.11078

Ann. Math. (2) 183, No. 3, 975-1014 (2016).
Summary: We generalize R. F. Coleman’s [Invent. Math. 124, No. 1–3, 215–241 (1996; Zbl 0851.11030)] classicity criterion for overconvergent modular forms on modular curves to the case of some PEL Shimura variety of type (A) or (C) associated to a reductive group unramified over \(\mathbb{Q}_p\). Our demonstration is inspired by the analytic continuation method of K. Buzzard [J. Am. Math. Soc. 16, No. 1, 29–55 (2003; Zbl 1076.11029)] and P. L. Kassaei [Duke Math. J. 132, No. 3, 509–529 (2006; Zbl 1112.11020)].

Cited in 12 Documents

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
11F85 \(p\)-adic theory, local fields
11F60 Hecke-Petersson operators, differential operators (several variables)

Keywords:

Coleman classicality criterion; Hecke operators; overconvergent modular forms; \(p\)-adic analytic continuation; rigid geometry

Citations:

Zbl 0851.11030; Zbl 1076.11029; Zbl 1112.11020
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\textit{S. Bijakowski} et al., Ann. Math. (2) 183, No. 3, 975--1014 (2016; Zbl 1407.11078)
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