Cohomology of Number Fields [electronic resource] /
Neukirch, Jürgen.author.
Schmidt, Alexander.author.
Wingberg, Kay.author.
The 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. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio
Description based upon print version of record.
The 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. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio
Includes bibliographical references and index.
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.
Number theory.
Algebraic geometry.
Group theory.
Number Theory.
Algebraic Geometry.
Group Theory and Generalizations.