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Class Field Theory - J. Neukirch
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J. Neukirch:

Class Field Theory - Paperback

2011, ISBN: 3642824676

[EAN: 9783642824678], Neubuch, [PU: Springer Berlin Heidelberg Dez 2011], GALOISTHEORY; RIEMANNZETAFUNCTION; VOLUME; ALGEBRA; ALGEBRAICNUMBERBOUNDARYELEMENTMETHOD; COHOMOLOGY; FIELDTHEORY… More...

NEW BOOK. Shipping costs:Versandkostenfrei. (EUR 0.00) BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany [57449362] [Rating: 5 (von 5)]
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Class Field Theory
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Class Field Theory - new book

ISBN: 9783642824678

Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by co… More...

Nr. 978-3-642-82467-8. Shipping costs:Worldwide free shipping, , zzgl. Versandkosten. (EUR 0.00)
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Class Field Theory - Neukirch, J.
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Neukirch, J.:
Class Field Theory - Paperback

2011

ISBN: 3642824676

Softcover reprint of the original 1st ed. 1986 Kartoniert / Broschiert Galoistheory; Riemannzetafunction; Volume; Algebra; algebraicnumberboundaryelementmethod; cohomology; fieldtheory;… More...

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J. Neukirch:
Class Field Theory (Grundlehren der mathematischen Wissenschaften) - Paperback

2011, ISBN: 9783642824678

Springer, 2011. Paperback. New. reprint edition. 150 pages. 9.25x6.10x0.36 inches., Springer, 2011, 6

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Class Field Theory - J. Neukirch
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J. Neukirch:
Class Field Theory - First edition

2011, ISBN: 9783642824678

Paperback

Buch, Softcover, Softcover reprint of the original 1st ed. 1986, [PU: Springer Berlin], Springer Berlin, 2011

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Details of the book
Class Field Theory

Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper- spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol- ogy, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group- theoretical principle, admitting an entirely elementary description. This de- scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep- tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here.

Details of the book - Class Field Theory


EAN (ISBN-13): 9783642824678
ISBN (ISBN-10): 3642824676
Hardcover
Paperback
Publishing year: 2011
Publisher: Springer Berlin

Book in our database since 2012-10-28T17:51:37+00:00 (London)
Detail page last modified on 2023-11-11T09:41:51+00:00 (London)
ISBN/EAN: 9783642824678

ISBN - alternate spelling:
3-642-82467-6, 978-3-642-82467-8
Alternate spelling and related search-keywords:
Book author: neukirch jürgen
Book title: class field theory


Information from Publisher

Author: J. Neukirch
Title: Grundlehren der mathematischen Wissenschaften; Class Field Theory
Publisher: Springer; Springer Berlin
142 Pages
Publishing year: 2011-12-15
Berlin; Heidelberg; DE
Printed / Made in
Language: English
85,59 € (DE)
87,99 € (AT)
94,50 CHF (CH)
POD
VIII, 142 p.

BC; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Galois theory; Riemann zeta function; Volume; algebra; algebraic number field; boundary element method; cohomology; field; field theory; finite group; form; homology; presentation; prime number; zeta function; Number Theory; BB; EA

I. Group and Field Theoretic Foundations.- § 1. Infinite Galois Theory.- § 2. Profinite Groups.- § 3. G-Modules.- § 4. The Herbrand Quotient.- § 5. Kummer Theory.- II. General Class Field Theory.- § 1. Frobenius Elements and Prime Elements.- § 2. The Reciprocity Map.- § 3. The General Reciprocity Law.- § 4. Class Fields.- § 5. Infinite Extensions.- III. Local Class Field Theory.- § 1. The Class Field Axiom.- § 2. The Local Reciprocity Law.- § 3. Local Class Fields.- § 4. The Norm Residue Symbol over Qp.- § 5. The Hilbert Symbol.- § 6. Formal Groups.- § 7. Fields of ?n-th Division Points.- § 8. Higher Ramification Groups.- § 9. The Weil Group.- IV. Global Class Field Theory.- § 1. Algebraic Number Fields.- § 2. Ideles and Idele Classes.- § 3. Galois Extensions.- § 4. Kummer Extensions.- § 5. The Class Field Axiom.- § 6. The Global Reciprocity Law.- § 7. Global Class Fields.- § 8. The Ideal-Theoretic Formulation of Class Field Theory.- § 9. The Reciprocity Law of Power Residues.- V. Zeta Functions and L-Series.- § 1. The Riemann Zeta Function.- § 2. The Dedekind Zeta Function.- § 3. The Dirichlet L-Series.- § 4. The Artin L-Series.- § 5. The Equality of Dirichlet L-Series and Artin L-Series.- § 6. Density Theorems.- Literature.

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