On The Main Conjectures Of Iwasawa Theory For Certain Elliptic Curves With Complex Multiplication

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On The Main Conjectures Of Iwasawa Theory For Certain Elliptic Curves With Complex Multiplication
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Author : Yukako Kezuka
language : en
Publisher:
Release Date : 2017
On The Main Conjectures Of Iwasawa Theory For Certain Elliptic Curves With Complex Multiplication written by Yukako Kezuka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Elliptic Curves Modular Forms And Iwasawa Theory
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Author : David Loeffler
language : en
Publisher: Springer
Release Date : 2017-01-15
Elliptic Curves Modular Forms And Iwasawa Theory written by David Loeffler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-15 with Mathematics categories.
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 Of Elliptic Curves With Complex Multiplication
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Author : Ehud De Shalit
language : en
Publisher:
Release Date : 1987
Iwasawa Theory Of Elliptic Curves With Complex Multiplication written by Ehud De Shalit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Noncommutative Iwasawa Main Conjectures Over Totally Real Fields
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Author : John Coates
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-19
Noncommutative Iwasawa Main Conjectures Over Totally Real Fields written by John Coates and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-19 with Mathematics categories.
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.
Integral Geometry Radon Transforms And Complex Analysis
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Author : Carlos A. Berenstein
language : en
Publisher: Springer
Release Date : 2006-11-14
Integral Geometry Radon Transforms And Complex Analysis written by Carlos A. Berenstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
Arithmetic Theory Of Elliptic Curves
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Author : J. Coates
language : en
Publisher: Springer
Release Date : 2006-11-14
Arithmetic Theory Of Elliptic Curves written by J. Coates and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.
Fifth International Congress Of Chinese Mathematicians
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Fifth International Congress Of Chinese Mathematicians written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
L Functions And Arithmetic
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Author : J. Coates
language : en
Publisher: Cambridge University Press
Release Date : 1991-02-22
L Functions And Arithmetic written by J. Coates and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-22 with Mathematics categories.
Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.
European Women In Mathematics Proceedings Of The 13th General Meeting
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Author : Sylvie Paycha
language : en
Publisher: World Scientific
Release Date : 2009-12-21
European Women In Mathematics Proceedings Of The 13th General Meeting written by Sylvie Paycha and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-21 with Mathematics categories.
This volume offers a unique collection of outstanding contributions from renowned women mathematicians who met in Cambridge for a conference under the auspices of European Women in Mathematics (EWM). These contributions serve as excellent surveys of their subject areas, including symplectic topology, combinatorics and number theory.The volume moreover sheds light on prominent women mathematicians who worked in Cambridge in the late 19th and early 20th centuries by providing an insightful historical introduction at the beginning of the volume.The volume concludes with short contributions from women mathematicians from across Europe working in various areas of mathematics ranging from group theory to magnetic fields.
Iwasawa Theory And Its Perspective Volume 1
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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-03
Iwasawa Theory And Its Perspective Volume 1 written by Tadashi Ochiai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-03 with Mathematics categories.
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.