TITLE: Motivic vs Deligne cohomology
QUESTION [12 upvotes]: Where can I find the construction of the cycle class map from motivic cohomology to Deligne cohomology of smooth projective varieties over the complex numbers?
It should be a construction by Bloch using his cycle complex, but it seems I can't find on the web any paper spelling it out.

REPLY [7 votes]: In addition to the papers mentioned, I would like to add Kerr, Lewis, Müller-Stach, The Abel–Jacobi map for higher Chow groups, Compositio (2006). They give an explicit construction (if you like that sort of thing -- I do), using currents, mapping a cubical Bloch complex to a complex computing Deligne cohomology. There is also a follow up paper by the first two authors (with obvious title) in Inventiones.