  Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse $t$-structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these $t$-structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse $t$-structures for
certain noncommutative projective planes.
