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Iwasawa Theory and Its Perspective, Volume 1
 
Tadashi Ochiai Tokyo Institute of Technology, Tokyo, Japan
Softcover ISBN:  978-1-4704-5672-6
Product Code:  SURV/272
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7325-9
Product Code:  SURV/272.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-5672-6
eBook: ISBN:  978-1-4704-7325-9
Product Code:  SURV/272.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
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Iwasawa Theory and Its Perspective, Volume 1
Tadashi Ochiai Tokyo Institute of Technology, Tokyo, Japan
Softcover ISBN:  978-1-4704-5672-6
Product Code:  SURV/272
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7325-9
Product Code:  SURV/272.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-5672-6
eBook ISBN:  978-1-4704-7325-9
Product Code:  SURV/272.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2722023; 154 pp
    MSC: Primary 11; 13;

    Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to \(p\)-adic \(L\)-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory.

    The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota \(L\)-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects.

    The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.

    Readership

    Graduate students and researchers interested in number theory and arithmetic geometry.

  • Table of Contents
     
     
    • Chapters
    • Motivation and utility of Iwasawa theory
    • $\mathbb {Z}_p$-extension and Iwasawa algebra
    • Cyclotomic Iwasawa theory for ideal class groups
    • Bookguide
    • Appendix A
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2722023; 154 pp
MSC: Primary 11; 13;

Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to \(p\)-adic \(L\)-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory.

The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota \(L\)-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects.

The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.

Readership

Graduate students and researchers interested in number theory and arithmetic geometry.

  • Chapters
  • Motivation and utility of Iwasawa theory
  • $\mathbb {Z}_p$-extension and Iwasawa algebra
  • Cyclotomic Iwasawa theory for ideal class groups
  • Bookguide
  • Appendix A
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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