Galois Cohomology and Class Field Theory
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra a...
| Autor principal: | |
|---|---|
| Autor Corporativo: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing
2020.
|
| Edición: | 1st ed |
| Colección: | Springer eBooks.
Universitext. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b43273798*spi |
| Sumario: | This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference. |
|---|---|
| Descripción Física: | XIV, 338 p. : 50 il., 2 il. col |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9783030439019 |
