Hopf Algebras Polynomial Formal Groups And Raynaud Orders
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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders
Author | : Lindsay Childs |
Publisher | : American Mathematical Soc. |
Total Pages | : 133 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821810774 |
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This volume 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.
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