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Noncommutative Iwasawa Main Conjectures Over Totally Real Fields
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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.
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 492 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.
Book Synopsis p-Adic Aspects of Modular Forms by : Baskar Balasubramanyam
Download or read book p-Adic Aspects of Modular Forms written by Baskar Balasubramanyam and published by World Scientific. This book was released on 2016-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n). Contents:An Overview of Serre's p-Adic Modular Forms (Miljan Brakočević and R Sujatha)p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine)Ordinary Families of Automorphic Forms on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar)Notes on Modularity Lifting in the Ordinary Case (David Geraghty)p-Adic L-Functions for Hilbert Modular Forms (Mladen Dimitrov)Arithmetic of Adjoint L-Values (Haruzo Hida)p-Adic L-Functions for GLn (Debargha Banerjee and A Raghuram)Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay A Burungale)The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh)Non-Commutative q-Expansions (Mahesh Kakde) Readership: Researchers in algebra and number theory.
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.
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 483 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).
Book Synopsis Win-- Women in Numbers by : Alina Carmen Cojocaru
Download or read book Win-- Women in Numbers written by Alina Carmen Cojocaru and published by American Mathematical Soc.. This book was released on 2011-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers on number theory which evolved out of the workshop WIN - Women in Numbers, held November 2nd-7th, 2008, in Alberta, Canada. The book includes articles showcasing outcomes from collaborative research initiated during the workshop.
Book Synopsis Algebraic Number Theory and Related Topics 2008 by : 中村博昭
Download or read book Algebraic Number Theory and Related Topics 2008 written by 中村博昭 and published by . This book was released on 2010 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Arithmetic of L-functions by : Cristian Popescu
Download or read book Arithmetic of L-functions written by Cristian Popescu and published by American Mathematical Soc.. This book was released on with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of His Sixtieth Birthday by : I. Fesenko
Download or read book A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of His Sixtieth Birthday written by I. Fesenko and published by American Mathematical Society(RI). This book was released on 2006 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Professor John H. Coates, an outstanding contributor to number theory, both through his pioneering and fundamental mathematical works and through the magnificent mathematical school he has established. It contains 24 articles written by 38 authors on a wide range of topics in the cutting edge of research in number theory, algebraic geometry and analysis: zeta functions and $L$-functions, automorphic and modularity issues, Galois representations,arithmetic of elliptic curves, Iwasawa theory, noncommutative Iwasawa theory, and $p$-adic analysis. This volume will be of interest to researchers and students in these and neighboring fields. Information for our distributors: A publication of the Documenta Mathematica. The AMS distributes this series,beginning with volume 3, in the United States, Canada, and Mexico.
Book Synopsis Stark's Conjectures: Recent Work and New Directions by : David Burns
Download or read book Stark's Conjectures: Recent Work and New Directions written by David Burns and published by American Mathematical Soc.. This book was released on 2004 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stark's conjectures on the behavior of $L$-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to Stark's conjectures. The remaining six contributions touch on some major themes currently under exploration in the area, such as non-abelian and $p$-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and Barry Mazur. The book is suitable for graduate students and researchers interested in number theory.
Book Synopsis Cyclotomic Fields and Zeta Values by : John Coates
Download or read book Cyclotomic Fields and Zeta Values written by John Coates and published by Springer Science & Business Media. This book was released on 2006-10-03 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two leading workers in the field, this brief but elegant book presents in full detail the simplest proof of the "main conjecture" for cyclotomic fields. Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. From the reviews: "The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details." --ZENTRALBLATT MATH
Book Synopsis A Collection of Manuscripts Written in Honour of Kazuya Kato on the Occasion of His Fiftieth Birthday by : Spencer Bloch
Download or read book A Collection of Manuscripts Written in Honour of Kazuya Kato on the Occasion of His Fiftieth Birthday written by Spencer Bloch and published by . This book was released on 2003 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Proceedings of the International Congress of Mathematicians by : Marta Sanz Solé
Download or read book Proceedings of the International Congress of Mathematicians written by Marta Sanz Solé and published by . This book was released on 2006 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.
Book Synopsis Development of Iwasawa Theory by : Masato Kurihara
Download or read book Development of Iwasawa Theory written by Masato Kurihara and published by Advanced Studies in Pure Mathe. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is edited as the proceedings of the international conference 'Iwasawa 2017', which was held at the University of Tokyo from July 19th through July 28th, 2017, in order to commemorate the 100th anniversary of Kenkichi Iwasawa's birth. In total 236 participants attended the conference including 98 participants from 15 countries outside Japan, and enjoyed the talks and the discussions on several themes flourishing in Iwasawa theory. This volume consists of 3 survey papers and of 15 research papers submitted from the speakers and the organizers of the conference. We also included 4 essays on memories of Iwasawa to celebrate the Centennial of Iwasawa's birth. We recommend this volume to all researchers and graduate students who are interested in Iwasawa theory, number theory and related fields.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
Download or read book Acta Arithmetica written by and published by . This book was released on 2013 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt:
