A perverse sheaf on a stratified space is a constructible complex of sheaves whose cohomology and Verdier-dual cohomology satisfy complementary dimension bounds along every stratum. With the middle perversity, these support and cosupport conditions place local cohomology in degrees determined by the codimension of the stratum.
Perverse sheaves form an Abelian category inside the derived category of constructible sheaves. The intersection cohomology complex of a singular algebraic variety is a fundamental example.
