This quantity includes the accelerated lectures given at a convention on quantity conception and mathematics geometry held at Boston college. It introduces and explains the numerous rules and strategies utilized by Wiles, and to provide an explanation for how his end result could be mixed with Ribets theorem and ideas of Frey and Serre to end up Fermats final Theorem. The publication starts off with an summary of the total evidence, through a number of introductory chapters surveying the fundamental concept of elliptic curves, modular features and curves, Galois cohomology, and finite staff schemes. illustration thought, which lies on the middle 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 ebook concludes via having a look either ahead and backward, reflecting at the heritage of the matter, whereas putting Wiles'theorem right into a extra basic Diophantine context suggesting destiny purposes. scholars mathematicians alike will locate this an quintessential source.
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