This quantity comprises the accelerated lectures given at a convention on quantity concept and mathematics geometry held at Boston college. It introduces and explains the numerous principles and strategies utilized by Wiles, and to provide an explanation for how his consequence might be mixed with Ribets theorem and concepts of Frey and Serre to end up Fermats final Theorem. The e-book starts off with an summary of the entire facts, through numerous introductory chapters surveying the fundamental thought of elliptic curves, modular features and curves, Galois cohomology, and finite staff schemes. illustration thought, which lies on the middle of the evidence, is handled in a bankruptcy on automorphic representations and the Langlands-Tunnell theorem, and this can be by means of in-depth discussions of Serres conjectures, Galois deformations, common deformation jewelry, Hecke algebras, and whole intersections. The publication concludes through having a look either ahead and backward, reflecting at the heritage of the matter, whereas putting Wiles'theorem right into a extra normal Diophantine context suggesting destiny purposes. scholars mathematicians alike will locate this an fundamental source.

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