Memoirs of the American Mathematical Society 1998; 118 pp; softcover Volume: 136 ISBN10: 0821810774 ISBN13: 9780821810774 List Price: US$47 Individual Members: US$28.20 Institutional Members: US$37.60 Order Code: MEMO/136/651
 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. Readership Advanced graduate students and research mathematicians working in formal groups, finite group schemes or local algebraic number theory and Galois module theory. Table of Contents  Introduction to polynomial formal groups and Hopf algebras
 Dimension one polynomial formal groups
 Dimension two polynomial formal groups and Hopf algebras
 Degree two formal groups and Hopf algebras
 \(p\)Elementary group schemesConstructions and Raynaud's theory
