9783642824678-3642824676-Class Field Theory (Grundlehren der mathematischen Wissenschaften (280))

Class Field Theory (Grundlehren der mathematischen Wissenschaften (280))

ISBN-13: 9783642824678
ISBN-10: 3642824676
Edition: Softcover reprint of the original 1st ed. 1986
Author: Neukirch, J.
Publication date: 2011
Publisher: Springer
Format: Paperback 150 pages
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Book details

ISBN-13: 9783642824678
ISBN-10: 3642824676
Edition: Softcover reprint of the original 1st ed. 1986
Author: Neukirch, J.
Publication date: 2011
Publisher: Springer
Format: Paperback 150 pages

Summary

Acknowledged authors Neukirch, J. wrote Class Field Theory (Grundlehren der mathematischen Wissenschaften (280)) comprising 150 pages back in 2011. Textbook and eTextbook are published under ISBN 3642824676 and 9783642824678. Since then Class Field Theory (Grundlehren der mathematischen Wissenschaften (280)) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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.

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