Iwasawa Theory And Its Perspective Volume 2 PDF Download
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Author | : Tadashi Ochiai |
Publisher | : American Mathematical Society |
Total Pages | : 228 |
Release | : 2024-04-25 |
Genre | : Mathematics |
ISBN | : 1470456737 |
Download Iwasawa Theory and Its Perspective, Volume 2 Book in PDF, ePub and Kindle
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.
Author | : Haruzo Hida |
Publisher | : World Scientific |
Total Pages | : 446 |
Release | : 2021-10-04 |
Genre | : Mathematics |
ISBN | : 9811241384 |
Download Elementary Modular Iwasawa Theory Book in PDF, ePub and Kindle
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.
Author | : Ellen Elizabeth Eischen |
Publisher | : American Mathematical Society |
Total Pages | : 199 |
Release | : 2024-03-26 |
Genre | : Mathematics |
ISBN | : 1470474921 |
Download Automorphic Forms Beyond $mathrm {GL}_2$ Book in PDF, ePub and Kindle
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
Author | : Thomas Appelquist |
Publisher | : Addison Wesley Publishing Company |
Total Pages | : 646 |
Release | : 1987 |
Genre | : Science |
ISBN | : |
Download Modern Kaluza-Klein Theories Book in PDF, ePub and Kindle
A comprehensive and impressive collection of original and translated papers by Kaluza, Klein, Einstein and others, carefully edited to place them in their historical and intellectual context.
Author | : Kazuya Kato |
Publisher | : American Mathematical Soc. |
Total Pages | : 243 |
Release | : 2000 |
Genre | : Class field theory |
ISBN | : 0821820958 |
Download Number Theory Book in PDF, ePub and Kindle
Author | : Kevin Costello |
Publisher | : American Mathematical Soc. |
Total Pages | : 264 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821852884 |
Download Renormalization and Effective Field Theory Book in PDF, ePub and Kindle
Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
Author | : Leonard Eugene Dickson |
Publisher | : |
Total Pages | : 330 |
Release | : 1901 |
Genre | : Galois field |
ISBN | : |
Download Linear Groups Book in PDF, ePub and Kindle
Author | : John R. Stallings |
Publisher | : |
Total Pages | : 71 |
Release | : 1971 |
Genre | : |
ISBN | : 9780608301099 |
Download Group Theory and Three Dimensional Manifolds Book in PDF, ePub and Kindle
Author | : Allen John Scott |
Publisher | : |
Total Pages | : 152 |
Release | : 1988 |
Genre | : Economic geography |
ISBN | : |
Download New Industrial Spaces Book in PDF, ePub and Kindle
Author | : Kazuya Kato |
Publisher | : American Mathematical Soc. |
Total Pages | : 180 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821808634 |
Download Number Theory 1 Book in PDF, ePub and Kindle
This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.