Filtrations on the homology of algebraic varieties /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Friedlander, E. M. (Eric M.), 1944- (Autor), Mazur, Barry (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island, United States : American Mathematical Society, 1994.
Colección:Memoirs of the American Mathematical Society ; Volume 110, no. 529.
Temas:
Algebraic cycles.
Filters (Mathematics)
Homology theory.
Cycles algébriques.
Filtres (Mathématiques)
Homologie.
Algebraic cycles
Homology theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Preface
  • Introduction
  • Chapter 1. Questions and Speculations
  • 1.1. The nitrations
  • 1.2. Dependence on the projective imbedding
  • 1.3. The Strong Lefschetz mapping in Lawson Homology
  • 1.4. Equivalence relations on algebraic cycles
  • 1.5. Stabilized homotopy of moduli spaces
  • 1.6. Joins and Resultants
  • Chapter 2. Abelian monoid varieties
  • 2.1. Monoids
  • 2.2. Limits
  • 2.3. Directed systems attached to an abelian monoid
  • 2.4. Limits of covariant functors
  • 2.5. Bi-algebras
  • 2.6. Abelian group completions
  • 2.7. Constructing limH*(m) from H*(M)2.8. Base points
  • 2.9. Primitive elements
  • 2.10. Mixed Hodge Structure
  • Chapter 3. Chow varieties and Lawson homology
  • 3.1. The Chow variety
  • 3.2. Functoriality and Chow varieties
  • 3.3. Functoriality: algebraic context
  • 3.4. The additive monoid
  • 3.5. Lawson homology
  • Chapter 4. Correspondences and Lawson homology
  • 4.1. Correspondence homomorphisms
  • 4.2. The Chow correspondence homomorphism
  • 4.3. The Chow correspondence homomorphism and Lawson homology
  • Chapter 5. Multiplication of algebraic cycles5.1. The multiplicative structure on Chow varieties
  • 5.2. Bilinear pairings on group completions
  • 5.3. The multiplicative structure on Lawson homology
  • 5.4. The ring structure on Lawson homology of P[sup(0)]
  • Chapter 6. Operations in Lawson homology
  • 6.1. The structure of the algebra A
  • 6.2. A geometric description of s
  • 6.3. A homological description of iterates of s
  • 6.4. The connection between s and the correspondence homomorphism
  • ""6.5. The operator Ï?[sub(j)]and the Chow correspondence homomorphism""""6.6. The operator h""; ""Chapter 7. Filtrations""; ""7.1. The Hodge Filtration""; ""7.2. The Geometric filtration""; ""7.3. The Topological filtration""; ""7.4. The Correspondence subspace""; ""7.5. Equality of correspondence and topological filtrations""; ""Appendix A. Mixed Hodge Structures, Homology, and Cycle classes""; ""A.1. Mixed Hodge Structure on homology and cohomology""; ""A.2. Homology and cohomology of smooth varieties""; ""A.3. Cycle classes in homology""
  • A.4. Change of cycle class under l.c.i. morphismsA.5. Relation to birational change of correspondence
  • A.6. Correspondences and suspensions
  • Appendix B. Trace maps and the Dold-Thom Theorem
  • B.1. The inverse image mapping on homology attached to a weighted map
  • B.2. The Dold-Thom theorem
  • Appendix Q. On the group completion of a simplicial monoid
  • Q.1. Rings of fractions
  • Q.2. Grading of RS-[sup(1)]
  • Q.3. The Eilenberg-Moore spectral sequence
  • Q.4. A comparison lemma
  • Q.5. Good simplicial monoids
  • Q.6. Homology of the group completion

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