Iwasawa Theory And Its Perspective Volume 2
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Author |
: Tadashi Ochiai |
Publisher |
: American Mathematical Society |
Total Pages |
: 228 |
Release |
: 2024-04-25 |
ISBN-10 |
: 9781470456733 |
ISBN-13 |
: 1470456737 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai
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 is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Author |
: Tadashi Ochiai |
Publisher |
: American Mathematical Society |
Total Pages |
: 167 |
Release |
: 2023-05-03 |
ISBN-10 |
: 9781470456726 |
ISBN-13 |
: 1470456729 |
Rating |
: 4/5 (26 Downloads) |
Synopsis Iwasawa Theory and Its Perspective, Volume 1 by : Tadashi Ochiai
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.
Author |
: Ellen Elizabeth Eischen |
Publisher |
: American Mathematical Society |
Total Pages |
: 199 |
Release |
: 2024-03-26 |
ISBN-10 |
: 9781470474928 |
ISBN-13 |
: 1470474921 |
Rating |
: 4/5 (28 Downloads) |
Synopsis Automorphic Forms Beyond $mathrm {GL}_2$ by : Ellen Elizabeth Eischen
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
Author |
: Haruzo Hida |
Publisher |
: World Scientific |
Total Pages |
: 446 |
Release |
: 2021-10-04 |
ISBN-10 |
: 9789811241383 |
ISBN-13 |
: 9811241384 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Elementary Modular Iwasawa Theory by : Haruzo Hida
This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.
Author |
: Kazuya Kato |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 243 |
Release |
: 2000 |
ISBN-10 |
: 9780821820957 |
ISBN-13 |
: 0821820958 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Number Theory by : Kazuya Kato
Author |
: Kazuya Kato |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 180 |
Release |
: 2000 |
ISBN-10 |
: 082180863X |
ISBN-13 |
: 9780821808634 |
Rating |
: 4/5 (3X Downloads) |
Synopsis Number Theory 1 by : Kazuya Kato
This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.
Author |
: M. Ram Murty |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 162 |
Release |
: 2009-02-09 |
ISBN-10 |
: 9780821847749 |
ISBN-13 |
: 0821847740 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Introduction to $p$-adic Analytic Number Theory by : M. Ram Murty
This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
Author |
: Matheus C. Bortolan |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 246 |
Release |
: 2020-05-29 |
ISBN-10 |
: 9781470453084 |
ISBN-13 |
: 1470453088 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Attractors Under Autonomous and Non-autonomous Perturbations by : Matheus C. Bortolan
This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.
Author |
: |
Publisher |
: |
Total Pages |
: 1404 |
Release |
: 1985 |
ISBN-10 |
: STANFORD:36105015640464 |
ISBN-13 |
: |
Rating |
: 4/5 (64 Downloads) |
Synopsis Books in Series by :
Vols. for 1980- issued in three parts: Series, Authors, and Titles.
Author |
: |
Publisher |
: |
Total Pages |
: 1106 |
Release |
: 1994 |
ISBN-10 |
: OSU:32437010530190 |
ISBN-13 |
: |
Rating |
: 4/5 (90 Downloads) |
Synopsis Government Reports Annual Index by :