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On the modularity of elliptic curves over -adic exercises
Authors:Christophe Breuil  Brian Conrad  Fred Diamond  Richard Taylor
Institution:Département de Mathématiques, CNRS, Université Paris-Sud, 91405 Orsay cedex, France ; Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 ; Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454 ; Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Abstract:We complete the proof that every elliptic curve over the rational numbers is modular.

Keywords:Elliptic curve  Galois representation  modularity
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