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
Categories:
Wikimedia Foundation. 2010.
Look at other dictionaries:
Constructible set (topology) — For a Gödel constructive set, see constructible universe. In topology, a constructible set in a noetherian topological space is a finite union of locally closed sets. (A set is locally closed if it is the intersection of an open set and closed… … Wikipedia
Perverse sheaf — 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 stratified space, usually singular. This concept was introduced by Joseph … Wikipedia
Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… … Wikipedia
Local system — In mathematics, local coefficients is an idea from algebraic topology, a kind of half way stage between homology theory or cohomology theory with coefficients in the usual sense, in a fixed abelian group A , and general sheaf cohomology which,… … Wikipedia
List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Dmodule — In mathematics, a D module is a module over a ring D of differential operators. The major interest of such D modules is as an approach to the theory of linear partial differential equations. Since around 1970, D module theory has been built up,… … Wikipedia
Verdier duality — In mathematics, Verdier duality is a generalization of the Poincaré duality of manifolds to spaces with singularities. The theory was introduced by Jean Louis Verdier (1965), and there is a similar duality theory for schemes due to Grothendieck.… … Wikipedia
mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… … Universalium