 Constructible sheaf

In mathematics, a constructible sheaf is a sheaf of abelian groups over some topological space X, such that X is the union of a finite number of locally closed subsets on each of which the sheaf is a twisted constant sheaf. It is a generalization of constructible topology in classical algebraic geometry.
In ladic cohomology constructible sheaves are defined in a similar way (Deligne 1977, IV.3). A sheaf of abelian groups on a Noetherian scheme is called constructible if the scheme has a finite cover by subschemes on which the sheaf is locally constant constructible (meaning represented by an etale cover). The constructible sheaves form an abelian category.
References
 Deligne, Pierre, ed. (1977) (in French), Séminaire de Géométrie Algébrique du Bois Marie — Cohomologie étale (SGA 4^{1}⁄_{2}), Lecture notes in mathematics, 569, Berlin: SpringerVerlag, doi:10.1007/BFb0091516, ISBN 9780387080666, http://modular.fas.harvard.edu/sga/sga/4.5/index.html
 Dimca, Alexandru (2004), Sheaves in topology, Universitext, Berlin, New York: SpringerVerlag, ISBN 9783540206651, MR2050072
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