Geodesic
Deligne–Beilinson cycle maps for Lichtenbaum cohomology
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 187-212.

Voir la notice de l'article provenant de la source International Press of Boston

We define Deligne–Beilinson cycle maps for Lichtenbaum cohomology of arbitrary complex algebraic varieties and show that the analogues of the Abel–Jacobi theorem and the Lefschetz theorem on $(1, 1)$-cycles hold for any complex algebraic variety if we replace the divisor class group with Voevodsky’s motivic cohomology with compact supports. For more general indices, we study the torsion part of the cycle maps. We also characterize the algebraic part of Griffiths’s intermediate Jacobians by a universal property.
DOI : 10.4310/HHA.2019.v21.n1.a9
Classification : 14C30, 14F42, 19E15
Keywords: étale motivic cohomology, Deligne cohomology, cycle map 
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     author = {Tohru Kohrita},
     title = {Deligne{\textendash}Beilinson cycle maps for {Lichtenbaum} cohomology},
     journal = {Homology, homotopy, and applications},
     pages = {187--212},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2019},
     doi = {10.4310/HHA.2019.v21.n1.a9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a9/}
}
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Tohru Kohrita. Deligne–Beilinson cycle maps for Lichtenbaum cohomology. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 187-212. doi : 10.4310/HHA.2019.v21.n1.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a9/

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