| Titre : | Cohomology of number fields |
| Auteurs : | Jürgen Neukirch ; Alexander Schmidt ; Kay Wingberg |
| Type de document : | texte imprimé |
| Editeur : | Berlin : Springer-Verlag, 2000 |
| Collection : | Grundlehren der mathematischen wissenschaften |
| ISBN/ISSN/EAN : | 978-3-540-66671-4 |
| Format : | 1 Vol. (XV-699 p.) / 24 cm |
| Langues originales: | |
| Index. décimale : | 512 (Algèbre) |
| Catégories : | |
| Mots-clés: | Homologie Galois (Théorie de) Corps algébriques |
| Résumé : |
Galois modules over local and global fields form the main subject of this monograph, which can serve both as a textbook for students, and as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides the necessary algebraic background. The arithmetic part deals with Galois groups of local and global fields: local Tate duality, the structure of the absolute Galois group of a local field, extensions of global fields with restricted ramification, cohomology of the idèle and the idèle class groups, Poitou-Tate duality for finitely generated Galois modules, the Hasse principle, the theorem of Grundwald-Wang, Leopoldt's conjecture, Riemann's existence theorem for number fields, embedding problems, the theorems of Iwasawa and of Safarevic on solvable groups as Galois groups over global fields, Iwasawa theory of local and global number fields, and the characterization of number fields by their absolute Galois groups. |
| Note de contenu : |
Sommaire - Algebraic Theory. - Ch. I Cohomology of Profinite Groups 3. - Ch. II Some Homological Algebra 77. - Ch. III Duality Properties of Profinite Groups 113. - Ch. IV Free Products of Profinite Groups 201. - Ch. V Iwasawa Modules 221. - Ch. VI Galois Cohomology 289. - Ch. VII Cohomology of Local Fields 319. - Ch. VIII Cohomology of Global Fields 365. - Ch. IX The Absolute Galois Group of a Global Field 449. - Ch. X Restricted Ramification 509. - Ch. XI Iwasawa Theory of Number Fields 597. - Ch. XII Anabelian Geometry 661. - Literature 681. - Index 694. |
| Côte titre : |
S8/58350-58351 |
Exemplaires (2)
| Cote | Support | Localisation | Disponibilité |
|---|---|---|---|
| S8/58350 | Livre | Bibliothèque centrale | Disponible |
| S8/58351 | Livre | Bibliothèque centrale | Disponible |
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