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Lawson homology, morphic cohomology and Chow motives



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