Galoissche Theorie Der P-Erweiterungen

Name: Galoissche Theorie Der P-Erweiterungen
Brand: Springer
SKU: 9783540048930
Price: 3429.0 INR
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by Helmut Koch , I. R. Safarevic

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ISBN13: 9783540048930
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: January 1, 1970
Pages: 164
Original Price: EUR 46.68
Language: German
Edition: Softcover Repri
Item Weight: 291 grams
BISAC Subject(s): General

About The Book

In diesem Buch wird ein ziemlich junges Gebiet der algebraischen Zahlentheorie behandelt. Es geht um die algebraische Theorie der p-Erweiterungen, die sich in den letzten 25 Jahren entwickelte und jetzt einen Vollkommenheitsgrad erreicht hat, welcher eine systematische Darstellung im hochsten MaBe wiinschenswert erscheinen HiBt. Diese Richtung in der Arithmetik beschiiftigt sich mit der Theorie der endlichen Erweiterungen von Korpem arithmetischen Typs. Das sind die . )J-adischen Zahl- korper, die Korper der formalen Potenzreihen mit endlichen Konstantenkorpem, die algebraischen Zahlkorper und die algebraischen Funktionenkorper in einer Unbestimmten mit endlichem Konstantenkorper. Ihr Hauptziel besteht darin, tiber die Informationen hinauszugelangen, welche die klassische Klassenkorpertheorie liefert, die bekanntlich einen Dberblick tiber die Erweiterungen mit kommutativer Galoisscher Gruppe gibt. Die KommutativiHit der Galoisschen Gruppe ist dabei sehr wesentlich. Die Klassenkorpertheorie ist dadurch ideenmaBig eng verbunden mit einem weiten Kreis mathematischer Theorien: von der Theorie der Radikal- erweiterungen (die jetzt als Kummersche Theorie bezeichnet wird) bis zu topologischen Dualitatssatzen, der Theorie der abelschen und harmonischen Integrale und den Picard-Mannigfaltigkeiten. Die gruppentheoretische Grundlage aller dieser Fragen ist die Pontrjagin-Dualitat kommutativer Gruppen und ihrer Charaktergruppen. Es ist dies der Tell der Mathematik, den A. WElL als "abelsche Mathematik" bezeichnet hat. Bekanntlich ging HILBERT beim Aufbau der Klassenkorpertheorie von der Analogie zwischen algebraischen Zahl-und Funktionenkorpem, d. h. den Korpem der mero- morphen Funktionen auf kompakten Riemannschen Flachen, aus. Von diesem Gesichtspunkt aus muB eine "nichtkommutative" Verallgemeinerung der Klassen- korpertheorie der Untersuchung der Fundamentalgruppe einer Riemannschen Flache entsprechen, die bekanntlich nichtkommutativ ist.

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