Operations on $t$-structures and perverse coherent sheaves

We introduce the notions of consistent pairs and consistent chains of $t$-structures and prove that two consistent chains of $t$-structures generate a distributive lattice. The technique developed is then applied to the pairs of chains obtained from the standard $t$-structure on the derived category of coherent sheaves and the dual $t$-structure by means of the shift functor. This yields a family of $t$-structures whose hearts are known as perverse coherent sheaves.