TITLE: References - Voevodsky motives are the derived category of Nori motives?
QUESTION [6 upvotes]: First I would like to know if this has been worked out, and if the answer is affirmative I would like to know some references.

REPLY [5 votes]: Example 3.20 of "Tannaka duality for enhanced triangulated categories", arXiv: 1309:0637v4 says that this would be true for rational motives if a t-structure compatible with Betti realisation exists. By Theorem 3.4 of Hanamura's  "Mixed motives and algebraic cycles III" (MRL 1999), such a t-structure would follow from Grothendieck's standard conjectures, Murre's conjectures and a generalisation of the Beilinson-Soule vanishing conjecture.