Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

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