Perverse sheaf

Summary

A perverse sheaf on a complex algebraic variety or analytic space is an object of the derived category of constructible sheaves, see the definition. It satisfies dimension conditions on its cohomology sheaves and on those of its dual. Despite the name, a perverse sheaf is a complex of sheaves, not a single sheaf. Perverse sheaves form an abelian category, the heart of the perverse t-structure, introduced by Beilinson, Bernstein, Deligne and Gabber. They include the intersection cohomology complexes of Goresky and MacPherson, and by the Riemann–Hilbert correspondence they correspond to regular holonomic D-modules.