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  "body": "\n## Summary\n\nA perverse sheaf on a complex algebraic variety or analytic space is an object of the [[derived category|5ST7NVJFSM]] of constructible sheaves, see the [[definition|JYW9312EE6]].\nIt satisfies dimension conditions on its cohomology sheaves and on those of its dual.\nDespite the name, a perverse sheaf is a complex of sheaves, not a single sheaf.\nPerverse sheaves form an abelian category, the heart of the perverse [[t-structure|2GD9V7SA0E]], introduced by Beilinson, Bernstein, Deligne and Gabber.\nThey include the intersection cohomology complexes of Goresky and MacPherson, and by the [[Riemann–Hilbert correspondence|KMAEWSVGRS]] they correspond to regular holonomic D-modules.\n\n## Explanations\n\n### L1 human\n\nOn a smooth space, the constant sheaf, which assigns to each open set the locally constant functions on it, behaves well with respect to Poincaré duality.\nOn a singular space it does not.\nThe fix is to use complexes of sheaves with cohomology in several degrees, with rules about how large the support of each degree may be.\nThese rules are chosen so that the class of objects is preserved by duality.\nOn a smooth variety of dimension $d$, the constant sheaf placed in degree $-d$ is perverse, and so is the sheaf of a single point placed in degree $0$.\n",
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  "name": "Perverse sheaf",
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