This quantity includes the increased lectures given at a convention on quantity thought and mathematics geometry held at Boston college. It introduces and explains the various principles and strategies utilized by Wiles, and to give an explanation for how his end result will be mixed with Ribets theorem and concepts of Frey and Serre to end up Fermats final Theorem. The e-book starts with an summary of the total facts, by way of numerous introductory chapters surveying the fundamental concept of elliptic curves, modular capabilities and curves, Galois cohomology, and finite workforce schemes. illustration conception, which lies on the center of the evidence, is handled in a bankruptcy on automorphic representations and the Langlands-Tunnell theorem, and this can be through in-depth discussions of Serres conjectures, Galois deformations, common deformation earrings, Hecke algebras, and entire intersections. The booklet concludes through having 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 functions. scholars mathematicians alike will locate this an fundamental source.
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