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Galois Module Structure of Algebraic Integers: 1 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) - Tapa blanda
Sinopsis
In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.
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Reseña del editor
In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.
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- EditorialSpringer
- Año de publicación2011
- ISBN 10 3642688187
- ISBN 13 9783642688188
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas276
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Galois Module Structure of Algebraic Integers
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Springer Berlin Heidelberg Dez 2011, 2011
ISBN 10: 3642688187
ISBN 13: 9783642688188
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ('normal integral basis'). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools. 276 pp. Englisch. Nº de ref. del artículo: 9783642688188
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Galois Module Structure of Algebraic Integers
Publicado por
Springer Berlin Heidelberg, 2011
ISBN 10: 3642688187
ISBN 13: 9783642688188
Nuevo
Taschenbuch
Librería: AHA-BUCH GmbH, Einbeck, Alemania
Calificación del vendedor: 5 de 5 estrellas
Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ('normal integral basis'). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools. Nº de ref. del artículo: 9783642688188
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Galois Module Structure of Algebraic Integers (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
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Galois Module Structure of Algebraic Integers
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Springer Berlin Heidelberg, 2011
ISBN 10: 3642688187
ISBN 13: 9783642688188
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insight. Nº de ref. del artículo: 5068131
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Galois Module Structure of Algebraic Integers
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Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2011, 2011
ISBN 10: 3642688187
ISBN 13: 9783642688188
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Librería: buchversandmimpf2000, Emtmannsberg, BAYE, Alemania
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Taschenbuch. Condición: Neu. Neuware -In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ('normal integral basis'). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 276 pp. Englisch. Nº de ref. del artículo: 9783642688188
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Galois Module Structure of Algebraic Integers
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Galois Module Structure of Algebraic Integers (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a Series of Modern Surveys in Mathematics)
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