  We discuss the question of finding conditions on a derived equivalence
between two smooth projective varieties $X$ and $Y$ that imply that $X$ and $Y$
are birational. The types of conditions we consider are in the spirit of
finding categorical analogous of classical Torelli theorems. We study, in
particular, a notion of strongly filtered derived equivalence and study cases
where strongly filtered derived equivalence implies birationality. We also
consider an open variant of our main question.
