This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
ISBN: | 9780821810774 |
Publication date: | 30th October 1998 |
Author: | Lindsay Childs |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 118 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Algebra Groups and group theory Number theory |