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Filtrations on the Homology of Algebraic Varieties
Eric M. Friedlander and Barry Mazur
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Memoirs of the American Mathematical Society
1994; 110 pp; softcover
Volume: 110
ISBN-10: 0-8218-2591-7
ISBN-13: 978-0-8218-2591-4
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/110/529
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This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of "Lawson homology" for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck.

Readership

Graduate students familiar with algebraic geometry of algebraic topology as well as mathematicians with research interests in algebraic cycles.

Table of Contents

  • Introduction
  • Questions and speculations
  • Abelian monoid varieties
  • Chow varieties and Lawson homology
  • Correspondences and Lawson homology
  • "Multiplication" of algebraic cycles
  • Operations in Lawson homology
  • Filtrations
  • Appendix A. Mixed Hodge structures, homology, and cycle classes
  • Appendix B. Trace maps and the Dold-Thom theorem
  • Appendix Q. On the group completion of a simplicial monoid
  • Bibliography
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