Lindsay N. Childs
Description
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.
Read more
Genres
Science & Technology
Tags
Mathematics
Science & Math
Pure Mathematics
Reading Moods
Suspenseful & Thrilling
Contributors
No contributors specified
Publishing Info
Publisher
American Mathematical Society
Month-Year
Jun, 2000
ISBN
ISBN-13: 9780821821312
ISBN-10: 0821821318
Language
English
No. of Pages
215
Format
Hardcover
Awards & Recognition
No awards specified
Available at
No purchase options available
First Reviewed by
Claim the Book
Are you an author of this book?
Report
Found an issue or correction?