Iwasawa theory and its perspective. Volume 1
 Responsibility
 Tadashi Ochiai.
 Publication
 Providence : American Mathematical Society, [2023]
 Copyright notice
 ©2023
 Physical description
 1 online resource (ix, 154 pages) : illustraions.
 Series
 Mathematical surveys and monographs ; volume 272. 00765376
Online
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Description
Creators/Contributors
 Author/Creator
 Ochiai, Tadashi, 1972 author.
 落合, 理 (1972) author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Cover
 Title page
 Contents
 Preface
 Chapter 1. Motivation and utility of Iwasawa theory
 1.1. Fermat's last theorem and ideal class groups
 1.2. Important meaning of special values of Riemann's zeta function
 1.3. Mysterious analogy between function fields and number fields
 1.4. Wiles's proof and Iwasawa theory
 Chapter 2. ℤ_{ }extension and Iwasawa algebra
 2.1. Basics on ℤ_{ }extensions
 2.2. Definition of Iwasawa algebra and its various aspects
 2.3. Iwasawa modules
 Chapter 3. Cyclotomic Iwasawa theory for ideal class groups
 3.1. Algebraic aspect (Selmer group)
 3.2. Analytic aspect ( adic function)
 3.3. Bridge between the algebraic side and the analytic side (Iwasawa main conjecture)
 3.4. Iwasawa main conjecture for class groups over general base fields
 3.5. Problems and perspective beyond the Iwasawa main conjecture
 Bookguide
 Appendix A.
 A.1. Modular forms and associated Galois representations
 A.2. Algebraic Hecke characters and associated Galois characters
 References
 Index
 Back Cover
 Summary
 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 padic Lfunctions. 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.
Subjects
Bibliographic information
 Publication date
 2023
 Copyright date
 2023
 Series
 Mathematical surveys and monographs, 00765376 ; volume 272
 ISBN
 9781470473259 electronic book
 1470473259 electronic book
 9781470456726 (print)