Class Field Theory

From Theory to Practice

G. Gras

492 pages, parution le 29/11/2002

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Résumé

Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant (/cal T) p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory.

Contents

I. Basic Tools and Notations
II. Reciprocity Maps — Existence Theorems.
III. Abelian Extensions with Restricted Ramification—Abelian Closure
IV. Invariant Class Groups in p-Ramification — Genus Theory
V. Cyclic Extensions with Prescribed Ramification
Appendix: Arithmetical Interpretation of H²(G ^S_T , Z/p^eZ) .

L'auteur - G. Gras

Gras, G., University of Franche-Comte, Besancon, France

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	G. Gras
Parution	29/11/2002
Nb. de pages	492
Format	16 x 24
Couverture	Relié
Poids	860g
Intérieur	Noir et Blanc
EAN13	9783540441335