Cohomology of Number Fields

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.

List of contents

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.

Summary

In the words of a reviewer: “This monograph gives a very complete treatment of a vast array of cental topics in algebraic number theory
There is so much material written down systematically which was known to the experts, but whose detailed proof did not actually exist in the literature (most notable amongst these is the celebrated duality theorem of Poitou and Tate)”

Additional text

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

Report

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

Product details

• Authors: Jürge Neukirch, Jürgen Neukirch, Alexander Schmidt, Kay Wingberg
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2016
• EAN: 9783662517451
• ISBN: 978-3-662-51745-1
• No. of pages: 826
• Dimensions: 157 mm x 236 mm x 46 mm
• Weight: 1270 g
• Illustrations: XV, 826 p.
• Series: Grundlehren der mathematischen Wissenschaften; Grundlehren der mathematischen Wissenschaften
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, Gruppen und Gruppentheorie, Algebraische Geometrie, Group Theory, Mathematics and Statistics, Algebraic Geometry, Number Theory, Groups & group theory, Group Theory and Generalizations, Homological algebra, cohomology, finite group, cohomology theory