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Sinopsis
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. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.
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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.
In the corrected 2nd printing 2005, the author improves some mathematical and bibliographical details and adds a few pages about rank computations for the general reflection theorem; then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz for quadratic fields and for the p-th cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view.
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Class Field Theory: From Theory to Practice
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Springer, Berlin, 2003
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ISBN 13: 9783540441335
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Hardcover. Condición: Near fine. Springer Monographs in Mathematics. xiii, 491 p. 24 cm. Some wrinkling around hinges. Nº de ref. del artículo: 149665
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Class Field Theory : From Theory to Practice : (Reihe: SMM - Springer Monographs in Mathematics)
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Class Field Theory : From Theory to Practice
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Springer Berlin Heidelberg, 2005
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Class Field Theory: From Theory to Practice
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Springer-Verlag, 2003
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Class Field Theory
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Springer Berlin Heidelberg, 2002
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. This book explores the consequences and the practical use of these results in detailed studie. Nº de ref. del artículo: 4890875
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Class Field Theory: From Theory to Practice
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Class Field Theory
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Springer Berlin Heidelberg Nov 2002, 2002
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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) andlays 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.In the corrected 2nd printing 2005, the author improves some mathematical and bibliographical details and adds a few pages about rank computations for the general reflection theorem; then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz for quadratic fields and for the p-th cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view. 512 pp. Englisch. Nº de ref. del artículo: 9783540441335
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Class Field Theory : From Theory to Practice
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Springer Berlin Heidelberg, 2002
ISBN 10: 3540441336
ISBN 13: 9783540441335
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Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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) andlays 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.In the corrected 2nd printing 2005, the author improves some mathematical and bibliographical details and adds a few pages about rank computations for the general reflection theorem; then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz for quadratic fields and for the p-th cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view. Nº de ref. del artículo: 9783540441335
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Class Field Theory
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Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2002, 2002
ISBN 10: 3540441336
ISBN 13: 9783540441335
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Buch. Condición: Neu. Neuware -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. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 512 pp. Englisch. Nº de ref. del artículo: 9783540441335
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Class Field Theory: From Theory to Practice
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