Cohomology of Number Fields

Description

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) Front Matter....Pages i-xv Front Matter....Pages 1-1 Cohomology of Profinite Groups....Pages 3-96 Some Homological Algebra....Pages 97-145 Duality Properties of Profinite Groups....Pages 147-244 Free Products of Profinite Groups....Pages 245-266 Iwasawa Modules....Pages 267-333 Front Matter....Pages 335-335 Galois Cohomology....Pages 337-369 Cohomology of Local Fields....Pages 371-423 Cohomology of Global Fields....Pages 425-520 The Absolute Galois Group of a Global Field....Pages 521-597 Restricted Ramification....Pages 599-719 Iwasawa Theory of Number Fields....Pages 721-784 Anabelian Geometry....Pages 785-803 Back Matter....Pages 805-826