Cohomology of Number Fields (Grundlehren der mathematischen Wissenschaften) （2ND）

Neukirch, Jürgen/ Schmidt, Alexander/ Wingberg, Kay

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（2016/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 826 p.
• 言語 ENG
• 商品コード 9783662517451

Description

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)" 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.

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.