High Quality Content by WIKIPEDIA articles! The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space X, which may be a real or complex manifold, or a more general Topologically stratified space, usually singular. This concept was introduced by Zoghman Mebkhout in his thesis and then further developed by Joseph Bernstein, Alexander Beilinson, Pierre Deligne, and Ofer Gabber (1982) as a formalisation of the Riemann-Hilbert correspondence, which related the topology of singular spaces (intersection homology of Mark Goresky and Robert MacPherson) and the algebraic theory of differential equations (microlocal calculus and holonomic D-modules of Joseph Bernstein, Masaki Kashiwara and Takahira Kawai). It was clear from the outset that perverse sheaves are fundamental mathematical objects at the crossroads of algebraic geometry, topology, analysis and differential equations. They also play an important role in number theory, algebra, and representation theory.

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