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A modularity lifting theorem for weight two Hilbert modular forms. (English) Zbl 1185.11030
Summary: We prove a modularity lifting theorem for potentially Barsotti-Tate representations over totally real fields, generalising recent results of Kisin. Unfortunately, there was an error in the original version of this paper, meaning that we can only obtain a slightly weaker result in the case where the representations are potentially ordinary; an erratum has been added explaining this error.

11F33 Congruences for modular and \(p\)-adic modular forms
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F80 Galois representations
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