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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders
Lindsay N. Childs, State University of New York at Albany, NY, Cornelius Greither, Université Laval, Quebec, QC, Canada, David J. Moss, MapInfo Corporation, Troy, NY, Jim Sauerberg, Saint Mary's College, Moraga, CA, and Karl Zimmermann, Union College, Schenectady, NY
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Memoirs of the American Mathematical Society
1998; 118 pp; softcover
Volume: 136
ISBN-10: 0-8218-1077-4
ISBN-13: 978-0-8218-1077-4
List Price: US$47
Individual Members: US$28.20
Institutional Members: US$37.60
Order Code: MEMO/136/651
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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 schemes--Constructions and Raynaud's theory
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