  A conjecture of Orlov predicts that derived equivalent smooth projective
varieties over a field have isomorphic Chow motives. The conjecture is known
for curves, and was recently observed for surfaces by Huybrechts. In this paper
we focus on threefolds over perfect fields, and unconditionally secure results,
which are implied by Orlov's conjecture, concerning the geometric coniveau
filtration, and abelian varieties attached to smooth projective varieties.
