Galois Module Structure in Wild Extensions of the Rational Function Field PDF Download
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Author: Raymond Miller
Publisher:
ISBN:
Category :
Languages : en
Pages : 89
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Book Description
Author: Raymond Miller
Publisher:
ISBN:
Category :
Languages : en
Pages : 89
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Book Description
Author: Raymond Miller
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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: Victor Percy Snaith
Publisher: American Mathematical Soc.
ISBN: 082180264X
Category : Mathematics
Languages : en
Pages : 218
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Book Description
Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions.
Author: Patrick Hild
Publisher: Presses Univ. Franche-Comté
ISBN: 284867282X
Category :
Languages : en
Pages : 203
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Author: A. Fröhlich
Publisher: Springer
ISBN: 9783642688188
Category : Mathematics
Languages : en
Pages : 266
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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: 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: Sebastian Tomaskovic-Moore
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additive Galois modules, the ring of integers OL of L is studied as a module for the group ring OKG, where G is the Galois group of L/K. When K is a p-adic field, we also find a structure of OKG module when we replace OL with the group of points in OL of a Lubin-Tate formal group defined over K. For this new Galois module we find an analogue of the normal basis theorem. When K is a proper unramified extension of Qp , we show that some eigenspaces for the Teichmüller character are not free. We also adapt certain cases of E. Noether's result on normal integral bases for tame extensions. Finally, for wild extensions we define a version of Leopoldt's associated order and demonstrate in a specific case that it is strictly larger than the integral group ring.
Author: Simone Malacrida
Publisher: Simone Malacrida
ISBN:
Category : Mathematics
Languages : en
Pages : 63
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Book Description
The following topics are presented in this book: symmetric polynomials, symmetric functions, symmetric relations and Cauchy modules Galois group and Galois theory of equations binomial equations and fundamental theorem inverse Galois problem and Ruffini-Abel theorem resolutions of second, third, and fourth degree equations and monodromy
Author: Lauren Heller
Publisher:
ISBN:
Category : Galois modules (Algebra)
Languages : en
Pages : 46
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Book Description
If K/F is a Galois field extension with Galois group of prime power order distinct from char(F), then Gal(K/F) acts on pth power classes of K. The structure of the resulting module is known for Gal(K/F) isomorphic to a cyclic group of prime power order or the Klein 4-group. We use Artin-Schreier theory to produce a similar decomposition for characteristic p extensions with bicyclic Galois groups of exponent p.
