Deligne–Beilinson cycle maps for Lichtenbaum cohomology
Deligne–Beilinson cycle maps for Lichtenbaum cohomology
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 …