𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Cohomology of Number Fields

✍ Scribed by Jürgen Neukirch, Alexander Schmidt, Kay Wingberg (auth.)

Book ID
127455827
Publisher
Springer
Year
2008
Tongue
English
Weight
8 MB
Edition
2
Category
Library
City
Berlin; New York
ISBN
3540666710
ISSN
0072-7830

No coin nor oath required. For personal study only.

✦ Synopsis

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)

✦ Subjects

Group Theory and Generalizations

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✍ V. Suresh 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 290 KB

Let k be a field of characteristic not equal to 2. For nZ1; let H n ðk; Z=2Þ denote the nth Galois Cohomology group. The classical Tate's lemma asserts that if k is a number field then given finitely many elements a 1 ; ?; a n AH 2 ðk; Z=2Þ; there exist a; b 1 ; ?; b n Ak à such that a i ¼ ðaÞ,ðb i