Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders is written by Lindsay Childs and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821810774 (ISBN 10) and 9780821810774 (ISBN 13).

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.