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Memoirs of the American Mathematical Society
1998; 118 pp; softcover
List Price: US$50
Individual Members: US$30
Institutional Members: US$40
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.
Advanced graduate students and research mathematicians working in formal groups, finite group schemes or local algebraic number theory and Galois module theory.
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