Iwasawa theory and its perspective
著者
書誌事項
Iwasawa theory and its perspective
（Mathematical surveys and monographs, v. 272）
American Mathematical Society, 2023
- v. 1 : pbk
- タイトル別名
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Iwasawa riron to sono tenbou
岩澤理論とその展望
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注記
Originally published: Tokyo : Iwanami Shoten, 2014 and 2016
Includes bibliographical references (p. 145-151) and index
内容説明・目次
内容説明
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.
目次
Motivation and utility of Iwasawa theory
$\mathbb{Z}_p$-extension and Iwasawa algebra
Cyclotomic Iwasawa theory for ideal class groups
Bookguide
Appendix A
References
Index
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