Iwasawa Theory 2012 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Iwasawa Theory 2012 write by Thanasis Bouganis. This book was released on 2014-12-08. Iwasawa Theory 2012 available in PDF, EPUB and Kindle. 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).
Elliptic Curves, Modular Forms and Iwasawa Theory
Elliptic Curves, Modular Forms and Iwasawa Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves, Modular Forms and Iwasawa Theory write by David Loeffler. This book was released on 2017-01-15. Elliptic Curves, Modular Forms and Iwasawa Theory available in PDF, EPUB and Kindle. 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.
Number Theory
Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number Theory write by Kazuya Kato. This book was released on 2000. Number Theory available in PDF, EPUB and Kindle.
Noncommutative Iwasawa Main Conjectures over Totally Real Fields
Noncommutative Iwasawa Main Conjectures over Totally Real Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Iwasawa Main Conjectures over Totally Real Fields write by John Coates. This book was released on 2012-10-19. Noncommutative Iwasawa Main Conjectures over Totally Real Fields available in PDF, EPUB and Kindle. 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.
Introduction to Cyclotomic Fields
Introduction to Cyclotomic Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Cyclotomic Fields write by Lawrence C. Washington. This book was released on 2012-12-06. Introduction to Cyclotomic Fields available in PDF, EPUB and Kindle. 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.
