Filtrations on the Homology of Algebraic Varieties

ISBN-13: 9780821825914 / Angielski / Miękka / 1994

Il Evanston Eric M. (Northwestern University Friedlander; Barry Mazur

Opis

This work provides a detailed exposition of a classical topic. It describes 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.