Cohomology of Number Fields / Edition 2

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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.

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Editorial Reviews

From the Publisher

From the reviews of the second edition:

"The publication of a second edition gives me a chance to … emphasize what an important book it is. … the book a necessary part of the number theorist’s library. That it’s also well written, clear, and systematic is a very welcome bonus. … There are many goodies here … . it is an indispensable book for anyone working in number theory. … Neukirch, Schmidt, and Wingberg have, in fact, produced … authoritative, complete, careful, and sure to be a reliable reference for many years." (Fernando Q. Gouvêa, MathDL, May, 2008)

"The second edition will continue to serve as a very helpful and up-to-date reference in cohomology of profinite groups and algebraic number theory, and all the additions are interesting and useful. … the book is fine as it is: systematic, very comprehensive, and well-organised. This second edition will be a standard reference from the outset, continuing the success of the first one." (Cornelius Greither, Zentralblatt MATH, Vol. 1136 (14), 2008)

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Product Details

  • ISBN-13: 9783540378884
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 4/3/2008
  • Series: Grundlehren der mathematischen Wissenschaften Series, #323
  • Edition description: 2nd ed. 2008. Corr., 2nd printing 2013
  • Edition number: 2
  • Pages: 826
  • Product dimensions: 6.00 (w) x 9.40 (h) x 1.40 (d)

Table 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.

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