Constructible sheaf

From Wikipedia, the free encyclopedia

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.

The finiteness theorem in étale cohomology states that the higher direct images of a constructible sheaf are constructible.

References

Deligne, Pierre, ed. (1977), Séminaire de Géométrie Algébrique du Bois Marie — Cohomologie étale (SGA 4^1⁄₂), 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

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.