Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory - Couverture rigide

American Mathematical Society

Couverture rigide

ISBN 10 : 0821821318 ISBN 13 : 9780821821312

Editeur : American Mathematical Society, 2000

Synopsis

This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and, Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2000
• Langue: anglais
• ISBN 10: 0821821318
• ISBN 13: 9780821821312
• Reliure: Relié
• Nombre de pages: 215
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible