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Deligne-Beilinson cohomology. (English) Zbl 0656.14012
Beilinson’s conjectures on special values of L-functions, Meet. Oberwolfach/FRG 1986, Perspect. Math. 4, 43-91 (1988).
[For the entire collection see Zbl 0635.00005.]
Starting with a concrete description of the analytic Deligne cohomology for a curve, using the dilogarithm and Bloch’s regulator map, the Deligne-Beilinson complex and cohomology of a compactification of a quasiprojective complex manifold is described. Then the concept of a cycle class in this context is discussed, as well as the Abel-Jacobi map and Chern classes of a vector bundle are defined.
Reviewer: J.H.de Boer

MSC:
14F40 de Rham cohomology and algebraic geometry
14F99 (Co)homology theory in algebraic geometry