Iwasawa Theory Projective Modules And Modular Representations
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Iwasawa Theory Projective Modules And Modular Representations
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Author : Ralph Greenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Iwasawa Theory Projective Modules And Modular Representations written by Ralph Greenberg 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 2010 with Mathematics categories.
This paper shows that properties of projective modules over a group ring $\mathbf{Z}_p[\Delta]$, where $\Delta$ is a finite Galois group, can be used to study the behavior of certain invariants which occur naturally in Iwasawa theory for an elliptic curve $E$. Modular representation theory for the group $\Delta$ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a $\mu$-invariant. The author then studies $\lambda$-invariants $\lambda_E(\sigma)$, where $\sigma$ varies over the absolutely irreducible representations of $\Delta$. He shows that there are non-trivial relationships between these invariants under certain hypotheses.
Elementary Modular Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2021-10-04
Elementary Modular Iwasawa Theory written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-04 with Mathematics categories.
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.
Iwasawa Theory 2012
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Author : Thanasis Bouganis
language : en
Publisher: Springer
Release Date : 2014-12-08
Iwasawa Theory 2012 written by Thanasis Bouganis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-08 with Mathematics categories.
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
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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.
Hilbert Modular Forms And Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15
Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.
The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.
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language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N
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Author : Aleksandr Sergeevich Kleshchëv
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N written by Aleksandr Sergeevich Kleshchëv 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.
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Perspectives In Mathematical Science Ii Pure Mathematics
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Author : N S Narasimha Sastry
language : en
Publisher: World Scientific
Release Date : 2009-07-01
Perspectives In Mathematical Science Ii Pure Mathematics written by N S Narasimha Sastry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Mathematics categories.
This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics.
The Computational And Theoretical Aspects Of Elliptic Curves
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Author : Zhibin Liang
language : en
Publisher: Springer
Release Date : 2019-05-22
The Computational And Theoretical Aspects Of Elliptic Curves written by Zhibin Liang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-22 with Mathematics categories.
This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic. It provides an overview of the conjecture and a few special cases where the conjecture is proved. The broad theme of the two conferences was “Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture”. The first was held at Beijing International Centre for Mathematical Research (BICMR) in December 2014 and the second was held at the International Centre for Theoretical Sciences (ICTS), Bangalore, India in December 2016. Providing a broad overview of the subject, the book is a valuable resource for young researchers wishing to work in this area. The articles have an extensive list of references to enable diligent researchers to gain an idea of the current state of art on this conjecture.