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Elementary modular Iwasawa theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elementary modular Iwasawa theoryHaruzo Hida.
Author:	Hida, Haruzo.
Published:	Singapore :World Scientific,c2022.
Description:	1 online resource (448 p.)
Subject:	Iwasawa theory.
Online resource:	https://www.worldscientific.com/worldscibooks/10.1142/12398#t=toc
ISBN:	9789811241376$q(ebook)

Elementary modular Iwasawa theory
Hida, Haruzo.

Elementary modular Iwasawa theory[electronic resource] /Haruzo Hida. - Singapore :World Scientific,c2022. - 1 online resource (448 p.) - Series on number theory and its applications ;vol. 16. - Series on number theory and its applications ;v. 6..

Includes bibliographical references and index.

Cyclotomic Iwasawa theory -- Cuspidal Iwasawa theory -- Cohomological modular forms and p-adic L-functions -- p-adic families of modular forms -- Abelian deformation -- Universal ring and compatible system -- Cyclicity of adjoint Selmer groups -- Local indecomposability of modular Galois representation -- Analytic and topological methods.

"This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry. Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation. The fundamentals in the first five chapters are as follows: Iwasawa's proof; a modular version of Iwasawa's discovery by Kubert-Lang as an introduction to modular forms; a level-headed description of the p-adic interpolation of modular forms and p-adic L-functions, which are developed into a modular deformation theory; Galois deformation theory of the abelian case. The continuing chapters provide the level of exposition accessible to graduate students, while the results are the latest"--

Mode of access: World Wide Web.

ISBN: 9789811241376$q(ebook)Subjects--Topical Terms:

272965
Iwasawa theory.

LC Class. No.: QA247.3 / .H53 2022

Dewey Class. No.: 512.7/4

Elementary modular Iwasawa theory
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100 1 $a Hida, Haruzo. $3 575526
245 1 0 $a Elementary modular Iwasawa theory $h [electronic resource] / $c Haruzo Hida.
260 $a Singapore : $b World Scientific, $c c2022.
300 $a 1 online resource (448 p.)
490 1 $a Series on number theory and its applications ; $v vol. 16
504 $a Includes bibliographical references and index.
505 0 $a Cyclotomic Iwasawa theory -- Cuspidal Iwasawa theory -- Cohomological modular forms and p-adic L-functions -- p-adic families of modular forms -- Abelian deformation -- Universal ring and compatible system -- Cyclicity of adjoint Selmer groups -- Local indecomposability of modular Galois representation -- Analytic and topological methods.
520 $a "This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry. Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation. The fundamentals in the first five chapters are as follows: Iwasawa's proof; a modular version of Iwasawa's discovery by Kubert-Lang as an introduction to modular forms; a level-headed description of the p-adic interpolation of modular forms and p-adic L-functions, which are developed into a modular deformation theory; Galois deformation theory of the abelian case. The continuing chapters provide the level of exposition accessible to graduate students, while the results are the latest"-- $c Publisher's website.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Description based on print version record.
650 0 $a Iwasawa theory. $3 272965
650 0 $a Galois theory. $3 190982
650 0 $a Modules (Algebra) $3 190875
830 0 $a Series on number theory and its applications ; $v v. 6. $3 575543
856 4 0 $u https://www.worldscientific.com/worldscibooks/10.1142/12398#t=toc