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- W2951044918 abstract "We define Deligne-Beilinson cycle maps for Lichtenbaum cohomology $H_L^m(X, mathbb Z(n))$ and that with compact supports $H_{c,L}^m(X, mathbb Z(n))$ of an arbitrary complex algebraic variety $X.$ When $(m,n)=(2,1),$ the homological part of our cycle map with compact supports gives a generalization of the Abel-Jacobi theorem and its projection to the Betti cohomology yields that of the Lefschetz theorem on $(1,1)$-cycles for arbitrary complex algebraic varieties. In general degrees $(m,n),$ we show that the Deligne-Beilinson cycle maps are always surjective on torsion and have torsion-free cokernels. If $m leq 2n,$ the version with compact supports induces an isomorphism on torsion, and so does the one without compact supports if $min {2m-1, 2 dim X+1 } leq 2n.$ We also characterize the algebraic part of Griffiths's intermediate Jacobians with a universal property." @default.
- W2951044918 created "2019-06-27" @default.
- W2951044918 creator A5022828405 @default.
- W2951044918 date "2017-03-28" @default.
- W2951044918 modified "2023-09-27" @default.
- W2951044918 title "Deligne-Beilinson cycle maps for Lichtenbaum cohomology" @default.
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- W2951044918 hasPublicationYear "2017" @default.
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