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Author: Victor Percy Snaith
Publisher: American Mathematical Soc.
ISBN: 9780821871782
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This is the first published graduate course on the Chinburg conjectures, and this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.
Author: Victor Percy Snaith
Publisher: American Mathematical Soc.
ISBN: 9780821871782
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This is the first published graduate course on the Chinburg conjectures, and this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.
Author: Alfred Weiss
Publisher: American Mathematical Soc.
ISBN: 0821802658
Category : Mathematics
Languages : en
Pages : 106
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Book Description
This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Author: A. Fröhlich
Publisher: Springer Science & Business Media
ISBN: 3642688160
Category : Mathematics
Languages : en
Pages : 271
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Book Description
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.
Author: Albrecht Fröhlich
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Author: Lindsay N. Childs
Publisher: American Mathematical Soc.
ISBN: 1470465167
Category : Education
Languages : en
Pages : 311
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Book Description
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Author: Raymond Miller
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Bart De Smit
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
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Author: Frank A. Chemotti
Publisher:
ISBN:
Category : Field extensions (Mathematics)
Languages : en
Pages : 102
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Book Description
Author: Gove Griffith Elder
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
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Author: Martin John Taylor
Publisher:
ISBN:
Category : Galois theory
Languages : en
Pages : 162
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Book Description
