Iwasawa Theory 2012

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Iwasawa Theory 2012

Author : Thanasis Bouganis
Publisher : Springer
ISBN 13 : 3642552455
Total Pages : 487 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Iwasawa Theory 2012 by : Thanasis Bouganis

Download or read book Iwasawa Theory 2012 written by Thanasis Bouganis and published by Springer. This book was released on 2014-12-08 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).

Iwasawa Theory and Its Perspective, Volume 1

Author : Tadashi Ochiai
Publisher : American Mathematical Society
ISBN 13 : 1470456729
Total Pages : 167 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 1 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 1 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2023-05-03 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Curves, Modular Forms and Iwasawa Theory

Author : David Loeffler
Publisher : Springer
ISBN 13 : 3319450328
Total Pages : 494 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Elliptic Curves, Modular Forms and Iwasawa Theory by : David Loeffler

Download or read book Elliptic Curves, Modular Forms and Iwasawa Theory written by David Loeffler and published by Springer. This book was released on 2017-01-15 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.

Iwasawa Theory and Its Perspective, Volume 2

Author : Tadashi Ochiai
Publisher : American Mathematical Society
ISBN 13 : 1470456737
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Noncommutative Iwasawa Main Conjectures over Totally Real Fields

Author : John Coates
Publisher : Springer Science & Business Media
ISBN 13 : 3642321992
Total Pages : 216 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Noncommutative Iwasawa Main Conjectures over Totally Real Fields by : John Coates

Download or read book Noncommutative Iwasawa Main Conjectures over Totally Real Fields written by John Coates and published by Springer Science & Business Media. This book was released on 2012-10-19 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developed in the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered an important idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with an idea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The approach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideas in this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of some of the main general themes underlying these developments. The present volume will be a valuable resource for researchers working in both Iwasawa theory and the theory of automorphic forms.

Elementary Modular Iwasawa Theory

Author : Haruzo Hida
Publisher : World Scientific
ISBN 13 : 9811241384
Total Pages : 446 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Elementary Modular Iwasawa Theory by : Haruzo Hida

Download or read book Elementary Modular Iwasawa Theory written by Haruzo Hida and published by World Scientific. This book was released on 2021-10-04 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory

Author : Kazuya Kato
Publisher : American Mathematical Soc.
ISBN 13 : 0821820958
Total Pages : 243 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Number Theory by : Kazuya Kato

Download or read book Number Theory written by Kazuya Kato and published by American Mathematical Soc.. This book was released on 2000 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-abelian Fundamental Groups and Iwasawa Theory

Author : John Coates
Publisher : Cambridge University Press
ISBN 13 : 1139505653
Total Pages : 321 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Non-abelian Fundamental Groups and Iwasawa Theory by : John Coates

Download or read book Non-abelian Fundamental Groups and Iwasawa Theory written by John Coates and published by Cambridge University Press. This book was released on 2011-12-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Algebraic Geometry and Number Theory

Author : Hussein Mourtada
Publisher : Birkhäuser
ISBN 13 : 331947779X
Total Pages : 240 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Algebraic Geometry and Number Theory by : Hussein Mourtada

Download or read book Algebraic Geometry and Number Theory written by Hussein Mourtada and published by Birkhäuser. This book was released on 2017-05-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

A Theory of Generalized Donaldson-Thomas Invariants

Author : Dominic D. Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 0821852795
Total Pages : 212 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Theory of Generalized Donaldson-Thomas Invariants by : Dominic D. Joyce

Download or read book A Theory of Generalized Donaldson-Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

Higher Ramanujan Equations and Periods of Abelian Varieties

Author : Tiago J. Fonseca
Publisher : American Mathematical Society
ISBN 13 : 147046019X
Total Pages : 158 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Higher Ramanujan Equations and Periods of Abelian Varieties by : Tiago J. Fonseca

Download or read book Higher Ramanujan Equations and Periods of Abelian Varieties written by Tiago J. Fonseca and published by American Mathematical Society. This book was released on 2023-01-18 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Sage for Undergraduates

Author : Gregory V. Bard
Publisher : American Mathematical Society
ISBN 13 : 1470461552
Total Pages : 158 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sage for Undergraduates by : Gregory V. Bard

Download or read book Sage for Undergraduates written by Gregory V. Bard and published by American Mathematical Society. This book was released on 2022-09-26 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the open-source and free alternative to expensive software like Maple™, Mathematica®, and MATLAB®, Sage offers anyone with a web browser the ability to use cutting-edge mathematical software and share the results with others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students during Calculus II, Multivariate Calculus, Differential Equations, Linear Algebra, Math Modeling, or Operations Research. This book assumes no background in programming, but the reader who finishes the book will have learned about 60 percent of a first semester computer science course, including much of the Python programming language. The audience is not only math majors, but also physics, engineering, environmental science, finance, chemistry, economics, data science, and computer science majors. Many of the book's examples are drawn from those fields. Filled with “challenges” for the students to test their progress, the book is also ideal for self-study. What's New in the Second Edition: In 2019, Sage transitioned from Python 2 to Python 3, which changed the syntax in several significant ways, including for the print command. All the examples in this book have been rewritten to be compatible with Python 3. Moreover, every code block longer than four lines has been placed in an archive on the book's website http://www.sage-for-undergraduates.org that is maintained by the author, so that the students won't have to retype the code! Other additions include… The number of “challenges” for the students to test their own progress in learning Sage has roughly doubled, which will be a great boon for self-study.There's approximately 150 pages of new content, including: New projects on Leontief Input-Output Analysis and on Environmental ScienceNew sections on Complex Numbers and Complex Analysis, on SageTex, and on solving problems via Monte-Carlo Simulations.The first three sections of Chapter 1 have been completely rewritten to give absolute beginners a smoother transition into Sage.

Arithmetic and Geometry

Author : Luis Dieulefait
Publisher : Cambridge University Press
ISBN 13 : 1107462541
Total Pages : 539 pages
Book Rating : 4.1/5 (74 download)

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Book Synopsis Arithmetic and Geometry by : Luis Dieulefait

Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

The Story of Algebraic Numbers in the First Half of the 20th Century

Author : Władysław Narkiewicz
Publisher : Springer
ISBN 13 : 3030037541
Total Pages : 443 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis The Story of Algebraic Numbers in the First Half of the 20th Century by : Władysław Narkiewicz

Download or read book The Story of Algebraic Numbers in the First Half of the 20th Century written by Władysław Narkiewicz and published by Springer. This book was released on 2019-01-18 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Introduction to Cyclotomic Fields

Author : Lawrence C. Washington
Publisher : Springer Science & Business Media
ISBN 13 : 1461219345
Total Pages : 504 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Cyclotomic Fields by : Lawrence C. Washington

Download or read book Introduction to Cyclotomic Fields written by Lawrence C. Washington and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.

Deformation Theory and Local-Global Compatibility of Langlands Correspondences

Author : Martin Luu
Publisher : American Mathematical Soc.
ISBN 13 : 1470414228
Total Pages : 116 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Deformation Theory and Local-Global Compatibility of Langlands Correspondences by : Martin Luu

Download or read book Deformation Theory and Local-Global Compatibility of Langlands Correspondences written by Martin Luu and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.