Filtrations on the Homology of Algebraic Varieties.

Intro -- 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 cycles -- 5.1. 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 σ[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. morphisms -- A.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 -- Q.7. Applications to K-theory -- Q.8. A theorem of Mather -- Q.9. The group completion theorem in Segal's setup -- References for Appendix Q -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.