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AG (Algebraic geometry)
Mixed
See Friedlander and Voevodsky: http://www.math.uiuc.edu/K-theory/0075
See André, section 18.4
See also Motivic cohomology
http://mathoverflow.net/questions/42217/motivic-cohomology-vs-chow-for-singular-varieties
nLab page on Borel-Moore motivic homology