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Cohomology of Number Fields

Jürgen Neukirch, Alexander Schmidt, Kay Wingberg (Autoren)

Buch | Hardcover

XV, 826 Seiten

2008 | 2nd ed. 2008
Springer Berlin (Verlag)
978-3-540-37888-4 (ISBN)

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lt;p>This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.

Dr. Jürgen Neukirch, lehrt am Fachbereich Mathematik der Universität Regensburg.

Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic Theory: Galois Cohomology.- Cohomology of Local Fields.- Cohomology of Global Fields.- The Absolute Galois Group of a Global Field.- Restricted Ramification.- Iwasawa Theory of Number Fields.- Anabelian Geometry.- Literature.- Index.

ntralblatt MATH, Vol. 1136 (14), 2008)

Erscheint lt. Verlag	18.2.2008
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Zusatzinfo	XV, 826 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1278 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	11Gxx, 11Rxx, 11Sxx, 12Gxx, 14Hxx, 20Jxx • Algebra • algebraic number field • Algebraic Number Fields • algebraic number theory • arithmetic • cohomology • Cohomology theory • finite group • Galois-Feld • Galois group • Galois groups • Homological algebra • Kohomologie • Number Theory
ISBN-10	3-540-37888-X / 354037888X
ISBN-13	978-3-540-37888-4 / 9783540378884
Zustand	Neuware