Differences and relationships between Motivic cohomology (Beilinson, Lichtenbaum and Voevodsky) and Universal cohomology theory (Grothendieck)?
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1I know that motivic cohomology with rational coefficents should appear as particular Ext-groups in the category of motives. And that Motivic cohomology theory takes values in abelian groups, while the universal cohomology theory takes values in the still conjectural abelian category of mixed motives. – Aug 03 '14 at 05:50
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As far as I can tell, this is the same question as http://mathoverflow.net/questions/102839/what-is-the-relationship-between-motivic-cohomology-and-the-theory-of-motives?rq=1. – dhy Aug 03 '14 at 10:49