A map from Lawson homology to Deligne Cohomology
Wenchuan Hu

TL;DR
This paper constructs a natural map from Lawson homology to Deligne cohomology for smooth complex projective varieties using Harvey-Lawson spark complexes, and compares it to existing Abel-Jacobi type constructions.
Contribution
It introduces a new natural map connecting Lawson homology and Deligne cohomology, enhancing understanding of their relationship in algebraic geometry.
Findings
Established a map from Lawson homology to Deligne cohomology
Compared the new map with Abel-Jacobi type constructions
Provided insights into the relationship between these cohomological theories
Abstract
A natural map from Lawson homology to Deligne cohomology groups for smooth complex projective varieties is constructed by using the Harvey-Lawson spark complexes. We also compare this to Abel-Jacobi type constructions by others.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry
