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| 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 |
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| Softcover ISBN: | 978-1-4704-5672-6 |
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Book DetailsMathematical Surveys and MonographsVolume: 272; 2023; 154 ppMSC: 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.
ReadershipGraduate students and researchers interested in number theory and arithmetic geometry.
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Table of Contents
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Chapters
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Motivation and utility of Iwasawa theory
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$\mathbb {Z}_p$-extension and Iwasawa algebra
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Cyclotomic Iwasawa theory for ideal class groups
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Bookguide
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Appendix A
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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- Additional Material
- Requests
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.
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
