A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

ISBN-13: 9781108421775 / Angielski / Twarda / 2018 / 306 str.

Pierre Guillot

Opis

A self-contained exposition of local class field theory for students in advanced algebra.

Recenzje

'... a valuable book. I certainly cannot think of any other source that makes the basic ideas of class field theory, and the Kronecker-Weber theorems, more accessible. And the background material on noncommutative algebra and group cohomology can be read with profit by somebody just interested in these topics alone. Highly recommended.' Mark Hunacek, The Mathematical Gazette

Spis treści

Part I. Preliminaries: 1. Kummer theory; 2. Local number fields; 3. Tools from topology; 4. The multiplicative structure of local number fields; Part II. Brauer Groups: 5. Skewfields, algebras, and modules; 6. Central simple algebras; 7. Combinatorial constructions; 8. The Brauer group of a local number field; Part III. Galois Cohomology: 9. Ext and Tor; 10. Group cohomology; 11. Hilbert 90; 12. Finer structure; Part IV. Class Field Theory: 13. Local class field theory; 14. An introduction to number fields.