UID:
almahu_9947366445602882
Umfang:
1 online resource (599 p.)
ISBN:
1-281-76357-8
,
9786611763572
,
0-08-087394-4
Serie:
Pure and applied mathematics, a series of monographs and textbooks ; 78
Inhalt:
Formal groups and applications
Anmerkung:
Description based upon print version of record.
,
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
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8 The Lubin-Tate Formal Group LawsChapter 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
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15 Definitions. Survey of Results16 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
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24 Classification of One Dimensional Formal Group Laws over Finite Fields25 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
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30 ""Le Tapis de Cartier"" for Formal A-Modules, or Lifting Formal Group Laws and Formal A-Modules RevisitedE.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
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Chapter VII. Formal Groups and Bialgebras
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English
Weitere Ausg.:
ISBN 0-12-335150-2
Sprache:
Englisch
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