an introduction to non abelian class field theory

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An Introduction To Non Abelian Class Field Theory

Author : Toyokazu Hiramatsu
ISBN : 9789813142282
Genre : Mathematics
File Size : 71. 41 MB
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This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.

An Introduction To Non Abelian Class Field Theory

Author : Toyokazu Hiramatsu
ISBN : 9813142278
Genre : MATHEMATICS
File Size : 69. 32 MB
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"This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1."--Publisher's website.

An Introduction To Non Abelian Class Field Theory

Author : Toyokazu Hiramatsu
ISBN : 981314226X
Genre : Mathematics
File Size : 78. 33 MB
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This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.

Class Field Theory

Author : Nancy Childress
ISBN : 9780387724904
Genre : Mathematics
File Size : 20. 60 MB
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Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.

Local Class Field Theory

Author : Kenkichi Iwasawa
ISBN : UOM:39015015612537
Genre : History
File Size : 90. 19 MB
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This book provides a readable introduction to local class field theory, a theory of algebraic extensions. It covers abelian extensions in particular of so-called local fields, typical examples of which are the p-adic number fields. The book is almost self-contained and is accessible to any reader with a basic background in algebra and topological groups.

Local Fields And Their Extensions Second Edition

Author : Ivan B. Fesenko
ISBN : 9780821832592
Genre : Mathematics
File Size : 83. 12 MB
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This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.

Field Theory In Particle Physics

Author : B. de Wit
ISBN : 9780444596222
Genre : Technology & Engineering
File Size : 53. 14 MB
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``Field Theory in Particle Physics'' is an introduction to the use of relativistic field theory in particle physics. The authors explain the principal concepts of perturbative field theory and demonstrate their application in practical situations. The material presented in this book has been tested extensively in courses and the book is written in a lucid and engaging style. Many interesting problems are included at the end of each chapter, both to test the understanding of the subject matter and to further amplify the ideas in the text. The authors have taken great care to make their presentation as self-contained as possible by adding several appendices.

Conjectures In Arithmetic Algebraic Geometry

Author : Wilfred W. J. Hulsbergen
ISBN : 9783663095057
Genre : Technology & Engineering
File Size : 62. 48 MB
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In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.

A First Book Of Quantum Field Theory

Author : Amitabha Lahiri
ISBN : 0849338972
Genre : Science
File Size : 62. 11 MB
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This book introduces QFT for readers with no prior knowledge of the subject. It is meant to be a textbook for advanced undergraduate or beginning postgraduate students. The book discusses quantization of fields, S-matrix theory, Feynman diagrams, calculation of decay rates and cross sections, renormalization, symmetries and symmetry breaking. Some background material on classical field theory and group theory, needed for the exposition, are also presented in the book. Detailed calculations of weak and electromagnetic processes are included. There are many exercise problems to help the students, instructors and beginning researchers in the field. The second edition improves upon some notations and explanations, and includes answers to selected exercises.

Classical Field Theory

Author : Davison E. Soper
ISBN : 9780486462608
Genre : Science
File Size : 63. 68 MB
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This text concerns continuum mechanics, electrodynamics and the mechanics of electrically polarized media, and gravity. Geared toward advanced undergraduates and graduate students, it offers an accessible approach that formulates theories according to the principle of least action. The chief advantage of this formulation is its simplicity and ease, making the physical content of classical subjects available to students of physics in a concise form. Author Davison E. Soper, a Professor of Physics at the University of Oregon, intended this treatment as a primary text for courses in classical field theory as well as a supplement for courses in classical mechanics or classical electrodynamics. Topics include fields and transformation laws, the principle of stationary action, general features of classical field theory, the mechanics of fluids and elastic solids, special types of solids, nonrelativistic approximations, and the electromagnetic field. Additional subjects include electromagnetically polarized materials, gravity, momentum conservation in general relativity, and dissipative processes.

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