This quantity includes the extended lectures given at a convention on quantity conception and mathematics geometry held at Boston college. It introduces and explains the various principles and methods utilized by Wiles, and to provide an explanation for how his end result may be mixed with Ribets theorem and ideas of Frey and Serre to end up Fermats final Theorem. The e-book starts off with an summary of the whole evidence, via numerous introductory chapters surveying the fundamental idea of elliptic curves, modular capabilities 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 means 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 background of the matter, whereas putting Wiles'theorem right into a extra basic Diophantine context suggesting destiny functions. scholars mathematicians alike will locate this an necessary source.
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