Perverse sheaf

Definition

Let $X$ be a complex algebraic variety with a fixed algebraic stratification. A perverse sheaf on $X$ is an object of the heart

of the middle-perversity $t$-structure on the constructible derived category.

Equivalently, its ordinary cohomology sheaves obey the support and cosupport dimension inequalities. The shift is normalized so that a local system on a smooth complex variety of dimension $d$, placed in degree $d$, is perverse.