Formal Groups and Applications
Published on 23. November 1978
572 pages
978-0-08-087394-7 (ISBN)
Description
Formal Groups and Applications
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Michiel Hazewinkel
Formal Groups and Applications
Book
01/1978
Academic Press
€79.23
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Content
- Front Cover
- Formal Groups and Applications
- Copyright Page
- Contents
- Preface
- Leitfaden and Indicien
- Introduction
- Chapter I. Methods for Constructing One Dimensional Formal Groups
- 1 Definition and Elementary Properties of Formal Groups Survey of the Results of Chapter I
- 2 The Functional Equation-Integrality Lemma
- 3 The Formal Group Laws Fv(X, Y ), FV.T(X, Y ), and Fs ( X , Y)
- 4 Some Binomial Coefficient Arithmetic
- 5 A Universal One Dimensional Commutative Formal Group Law
- 6 Most One Dimensional Formal Group Laws Are Commutative
- 7 Honda's Method for Constructing Formal Group Laws
- 8 The Lubin-Tate Formal Group Laws
- Chapter II. Methods for Constructing Higher Dimensional Formal Group Laws
- 9 Definitions and Elementary Properties. Survey of the Results of Chapter II
- 10 The Higher Dimensional Functional Equation Lemma
- 11 The Universal n-Dimensional Commutative Formal Group Laws H u( X , Y )
- 12 Curvilinear Formal Group Laws
- 13 Higher Dimensional Honda Formal Group Laws and Higher Dimensional Lubin--Tate Formal Group Laws
- 14 Lie Theory
- E.1 Bibliographical and Other Notes
- Chapter III. Curves, p-Typical Formal Group Laws, and Lots of Witt Vectors
- 15 Definitions. Survey of Results
- 16 Curves and p-Typical Formal Groups
- 17 Lots of Witt Vectors
- E.2 Bibliographical and Other Notes
- Chapter IV. Homomorphisms, Endomorphisms, and the Classification of Formal Groups by Power Series Methods
- 18 Definitions and Preliminary Elementary Results. Survey of Chapter IV
- 19 Universal Isomorphisms
- 20 Existence and Nonexistence of Homomorphisms and Isomorphisms
- 21 Formal A-Modules
- 22 Lifting and Reducing Formal Group Laws. Formal Moduli
- 23 Rings of Endomorphisms of Formal Group Laws
- 24 Classification of One Dimensional Formal Group Laws over Finite Fields
- 25 Rings of Curves and Artin-Hasse-Like Exponential Mappings
- E.3 Bibliographical and Other Notes
- Chapter V. Cartier-Dieudonné Modules
- 26 Basic Definitions and Reminders. Survey of the Results of Chapter V
- 27 Cartier-Dieudonné Modules for Formal Group Laws
- 28 On the Classification of Commutative Formal Group Laws over an Algebraically Closed Field of Characteristic p & 0
- 29 Cartier-Dieudonné Theory for Formal A -Modules
- 30 "Le Tapis de Cartier" for Formal A-Modules, or Lifting Formal Group Laws and Formal A-Modules Revisited
- E.4 Bibliographical and Other Notes
- Chapter VI. Applications of Formal Groups in Algebraic Topology, Number Theory, and Algebraic Geometry
- 31 Basic Definitions and Survey of the Results of Chapter VI
- 32 Local Class Field Theory
- 33 Zeta Functions of Elliptic Curves over Q and Atkin--Swinnerton-Dyer Conjectures
- 34 On Complex Cobordism and Brown-Peterson Cohomology
- 35 Tate Modules (for One Dimensional Formal Group Laws)
- E.5 Bibliographical and Other Notes
- Chapter VII. Formal Groups and Bialgebras
- 36 Basic Definitions and Survey of the Results of Chapter VII
- 37 Formal Groups and Bialgebras
- 38 Curves in Noncommutative Formal Groups
- E.6 Bibliographical and Other Notes
- Appendix A. On Power Series Rings
- A.1 Power Series Rings
- A.2 Filtration and Topology
- A.3 Formal Weierstrass Preparation Theorem
- A.4 Homomorphisms and Isomorphisms. Formal Inverse Function and Implicit Function Theorems
- Appendix B. Brief Notes on Further Applications of Formal Group (Law) Theory
- B.1 More on Formal Groups in Number Theory
- B.2 More on Formal Groups in Algebraic Geometry
- B.3 More on Formal Groups in Arithmetical Algebraic Geometry
- B.4 More on Formal Groups in Algebraic Topology
- Bibliography
- Notation
- Index
- Pure and Applied Mathematics
