Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (Mathematical Surveys and Monographs) - Hopf Algebras and Local Galois Module Theory - Lindsay Childs (2000)
ISBN 0821821318
Subject Hopf algebras; Galois modules (Algebra); Field extensions (Mathematics)
Publisher American Mathematical Society
Publication Date May 2000
Format Hardcover (260 x 178 mm)
Language e
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.

Personal Details
Collection Status In Collection
Index 172
Read It Yes
Links Amazon US
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Product Details
LoC Classification QA613.8.C48 2000
Dewey 512/.55
Cover Price $57.00
No. of Pages 215