This quantity includes the multiplied lectures given at a convention on quantity thought and mathematics geometry held at Boston college. It introduces and explains the various rules and methods utilized by Wiles, and to provide an explanation for how his end result might be mixed with Ribets theorem and ideas of Frey and Serre to turn out Fermats final Theorem. The publication starts with an outline of the full evidence, by way of numerous introductory chapters surveying the elemental idea of elliptic curves, modular services 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 can be via in-depth discussions of Serres conjectures, Galois deformations, common deformation jewelry, Hecke algebras, and whole intersections. The e-book concludes by way of having a look either ahead and backward, reflecting at the heritage of the matter, whereas putting Wiles'theorem right into a extra common Diophantine context suggesting destiny functions. scholars mathematicians alike will locate this an integral source.

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