Iwasawa Theory and Its Perspective

Volumes 1-3

Tadashi Ochai

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Paperback

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English

American Mathematical Society
31 August 2025

Algebra; Number theory; Algebraic geometry

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, comprised of three volumes, was the need for a total perspective that includes the new trends of generalized Iwasawa theory. Another motivation is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory.

Volume 1: explains 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.

Volume 2: explains various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.

Volume 3: presents additional aspects of the Iwasawa theory of $p$-adic Galois deformations.

By: Tadashi Ochai
Imprint: American Mathematical Society
Country of Publication: United States [Currently unable to ship to USA: see Shipping Info]
ISBN: 9781470481773
ISBN 10: 1470481774
Pages: 489
Publication Date: 31 August 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Tadashi Ochai, Tokyo Institute of Technology, Japan