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Modular forms and Galois cohomology

Hida, Haruzo.

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Modular forms and Galois cohomology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Modular forms and Galois cohomology/ Haruzo Hida.
其他題名:	Modular Forms & Galois Cohomology
作者:	Hida, Haruzo.
出版者:	Cambridge :Cambridge University Press, : 2000.,
面頁冊數:	x, 343 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Forms, Modular. -
電子資源:	https://doi.org/10.1017/CBO9780511526046
ISBN:	9780511526046

Modular forms and Galois cohomology
Hida, Haruzo.

Modular forms and Galois cohomology[electronic resource] /Modular Forms & Galois CohomologyHaruzo Hida. - Cambridge :Cambridge University Press,2000. - x, 343 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;69. - Cambridge studies in advanced mathematics ;69..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Overview of Modular Forms.1.

This book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. It contains a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula and includes several new results from the author. The book will be of interest to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.

ISBN: 9780511526046Subjects--Topical Terms:

540521
Forms, Modular.

LC Class. No.: QA243 / .H43 2000

Dewey Class. No.: 512.73

Modular forms and Galois cohomology
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g 1. $t Overview of Modular Forms. $g 1.1. $t Hecke Characters. $g 1.2. $t Introduction to Modular Forms -- $g 2. $t Representations of a Group. $g 2.1. $t Group Representations. $g 2.2. $t Pseudo-representations. $g 2.3. $t Deformation of Group Representations -- $g 3. $t Representations of Galois Groups and Modular Forms. $g 3.1. $t Modular Forms on Adele Groups of GL(2). $g 3.2. $t Modular Galois Representations -- $g 4. $t Cohomology Theory of Galois Groups. $g 4.1. $t Categories and Functors. $g 4.2. $t Extension of Modules. $g 4.3. $t Group Cohomology Theory. $g 4.4. $t Duality in Galois Cohomology -- $g 5. $t Modular L-Values and Selmer Groups. $g 5.1. $t Selmer Groups. $g 5.2. $t Adjoint Selmer Groups. $g 5.3. $t Arithmetic of Modular Adjoint L-Values. $g 5.4. $t Control of Universal Deformation Rings.
520 $a This book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. It contains a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula and includes several new results from the author. The book will be of interest to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.
650 0 $a Forms, Modular. $3 540521
650 0 $a Galois theory. $3 523821
650 0 $a Homology theory. $3 555733
830 0 $a Cambridge studies in advanced mathematics ; $v 69. $3 3470692
856 4 0 $u https://doi.org/10.1017/CBO9780511526046