Filtrations on the Homology of Algebraic Varieties

Download or read book Filtrations on the Homology of Algebraic Varieties written by Eric M. Friedlander and published by American Mathematical Soc.. This book was released on 1994 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.