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Lawson homology, morphic cohomology and Chow motives
Author(s) -
Hu Wenchuan,
Li Li
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810283
Subject(s) - mathematics , cohomology , quotient , homology (biology) , pure mathematics , projective test , cellular homology , algebra over a field , biochemistry , chemistry , gene
In this paper, Lawson homology and morphic cohomology are defined for Chow motives. As consequences, we rederive the projective bundle formula proved by Friedlander and Gabber, the blowup formula for Lawson homology by the first author, and a formula for certain homogeneous projective varieties, including those admitting cellular decompositions. We also define rational coefficient Lawson homology and morphic cohomology for Chow motives of finite quotient varieties. As a consequence, we obtain a formula for the Hilbert scheme of points on a smooth complex projective surface. We also discuss generic finite maps, in particular, we give examples of self‐product of smooth projective curves with nontrivial Griffiths groups by using a result of Ceresa. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim