This quantity includes the accelerated lectures given at a convention on quantity concept and mathematics geometry held at Boston collage. It introduces and explains the numerous rules and methods utilized by Wiles, and to provide an explanation for how his outcome might be mixed with Ribets theorem and ideas of Frey and Serre to turn out Fermats final Theorem. The publication starts with an summary of the full evidence, via a number of introductory chapters surveying the fundamental idea of elliptic curves, modular capabilities and curves, Galois cohomology, and finite crew schemes. illustration idea, which lies on the center of the facts, is handled in a bankruptcy on automorphic representations and the Langlands-Tunnell theorem, and this is often by way of in-depth discussions of Serres conjectures, Galois deformations, common deformation jewelry, Hecke algebras, and entire intersections. The booklet concludes by way of taking a look either ahead and backward, reflecting at the historical past 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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