- 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.
- 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
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. 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
D-module — 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