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 l-adic 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 étale cover). The constructible sheaves form an abelian category.
- Deligne, Pierre, ed. (1977), Séminaire de Géométrie Algébrique du Bois Marie — Cohomologie étale (SGA 41⁄2), Lecture notes in mathematics (in French) 569 (569), Berlin: Springer-Verlag, doi:10.1007/BFb0091516, ISBN 978-0-387-08066-6
- Dimca, Alexandru (2004), Sheaves in topology, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-3-540-20665-1, MR 2050072
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