A Gentle Course in Local Class Field Theory PDF Download
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Author: Pierre Guillot
Publisher: Cambridge University Press
ISBN: 1108386261
Category : Mathematics
Languages : en
Pages : 309
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Book Description
This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker–Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.
Author: Pierre Guillot
Publisher: Cambridge University Press
ISBN: 1108386261
Category : Mathematics
Languages : en
Pages : 309
Get Book
Book Description
This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker–Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.
Author: Pierre Guillot
Publisher: Cambridge University Press
ISBN: 1108421776
Category : Mathematics
Languages : en
Pages : 309
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Book Description
A self-contained exposition of local class field theory for students in advanced algebra.
Author: C. P. Burgess
Publisher: Cambridge University Press
ISBN: 0521195470
Category : Science
Languages : en
Pages : 665
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Book Description
This advanced, accessible textbook on effective field theories uses worked examples to bring this important topic to a wider audience.
Author: Michael E. Peskin
Publisher: CRC Press
ISBN: 0429983182
Category : Science
Languages : en
Pages : 866
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Book Description
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
ISBN: 9780521004237
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author: Dinakar Ramakrishnan
Publisher: Springer Science & Business Media
ISBN: 1475730853
Category : Mathematics
Languages : en
Pages : 372
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Book Description
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
Author: Kevin Costello
Publisher: Cambridge University Press
ISBN: 1107163102
Category : Mathematics
Languages : en
Pages : 399
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Book Description
This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
Author: 健爾·上野
Publisher: American Mathematical Soc.
ISBN: 0821808621
Category : Geometry, Algebraic
Languages : en
Pages : 178
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Book Description
By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
Author: Tom Banks
Publisher: Cambridge University Press
ISBN: 1139473891
Category : Science
Languages : en
Pages : 323
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Book Description
Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.
Author: James F. Davis
Publisher: American Mathematical Society
ISBN: 1470473682
Category : Mathematics
Languages : en
Pages : 385
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Book Description
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
