Overview

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)""

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9783662517451

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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. Gouvea, 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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