Operations on \(t\)-structures and perverse coherent sheaves (Q2854091)

Let \(\mathcal{D}\) be a triangulated category. In this paper, the author considers the set of \(t\)-structures on \(\mathcal{D}\) and the natural partial order given and binary operations given on it by intersection and union. In order to show the existence of arbitrary unions and intersections, lower (resp. upper) consistent pairs of \(t\)-structures are defined by imposing consistency of the first (resp. the second) one with respect to the truncation functor coming from the second (resp. the first) one. Modular laws for the lattice are described, and an application to perverse sheaves on a smooth projective variety in characteristic zero is detailed in the last section.