Lawson homology, morphic cohomology and Chow motives

In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a consequence, we obtain a formula for the Hilbert scheme of points on a smooth complex projective surface. Further discussion concerning generic finite maps is given. As a result, we give examples of self-product of smooth projective curves with nontrivial Griffiths groups by using a result of Ceresa.

💡 Research Summary

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The paper develops a unified framework that places Lawson homology and morphic cohomology inside the category of Chow motives. A Chow motive is a triple (X, p, m) where X is a smooth projective variety, p is an algebraic correspondence of codimension m, and m is an integer weight. The authors construct two functors
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