Perverse coherent sheaves

This note introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on an algebraic stack (subject to some mild technical conditions). Under additional assumptions construction of coherent “intersection cohomology” sheaves is given. Those latter assumptions are rather restrictive but hold in some examples of interest in representation theory.
Similar results were obtained by Deligne (unpublished), Gabber and Kashiwara.