Galois Module Structure of Lubin-Tate Modules PDF Download
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Author: Sebastian Tomaskovic-Moore
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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: 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: Chan Shih-Ping
Publisher:
ISBN:
Category :
Languages : en
Pages : 8
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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: Peter Schneider
Publisher: Cambridge University Press
ISBN: 110718858X
Category : Mathematics
Languages : en
Pages : 157
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Book Description
A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.
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: Laurent Berger
Publisher: American Mathematical Soc.
ISBN: 1470440733
Category : Education
Languages : en
Pages : 75
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Book Description
The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.
Author: F. Halter-Koch
Publisher: Walter de Gruyter
ISBN: 3110801957
Category : Mathematics
Languages : en
Pages : 573
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Patrick Hild
Publisher: Presses Univ. Franche-Comté
ISBN: 284867282X
Category :
Languages : en
Pages : 203
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Author: S-P. Chan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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