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 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 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 4¹⁄₂), Lecture notes in mathematics, 569, Berlin: Springer-Verlag, doi:10.1007/BFb0091516, ISBN 978-0-387-08066-6, http://modular.fas.harvard.edu/sga/sga/4.5/index.html 
• Dimca, Alexandru (2004), Sheaves in topology, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-3-540-20665-1, MR2050072