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Modularity of certain potentially Barsotti-Tate Galois representations. (English) Zbl 0923.11085
The paper under review extends the technique of Wiles-Taylor to show that certain Galois representations are modular. For example, the main result implies that any elliptic curve over the rationals with conductor not divisible by 27 is modular. In the proof one defines certain types of Galois representations (quite technical), shows that they arise from modular forms, and finally that this gives the universal deformation.
Reviewer: G.Faltings (Bonn)

MSC:
11F80 Galois representations
11G18 Arithmetic aspects of modular and Shimura varieties
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