andrew wiles fermat last theorem pdf viewer

In the first volume the modularity lifting theorem on Galois representations has been reduced to properties of the deformation rings and the Hecke modules. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof. Here the detail of the proof announced in the first volume is fully exposed. This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series see MMONO/243). Students and professional mathematicians alike will find this an indispensable resource. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University.

Andrew wiles fermat last theorem pdf viewer