the sheaf theory

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• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

• Sheaf cohomology — In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. This is the main step, in… …   Wikipedia

• Sheaf extension — In Sheaf theory (a branch of the mathematics area of algebraic geometry), a sheaf extension is a way of describing a sheaf in terms of a subsheaf and a quotient sheaf, analogous to a how a group extension describes a group in terms of a subgroup …   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

• Sheaf spanned by global sections — In mathematics, a sheaf spanned by global sections is a sheaf F on a locally ringed space X , with structure sheaf O X that is of a rather simple type. Assume F is a sheaf of abelian groups. Then it is asserted that if A is the abelian group of… …   Wikipedia

• Twistor theory — The twistor theory, originally developed by Roger Penrose in 1967, is the mathematical theory which maps the geometric objects of the four dimensional space time (Minkowski space) into the geometric objects in the 4 dimensional complex space with …   Wikipedia

• The Motorcycle Diaries (book) — This article is about the book. For the movie based on the book, see The Motorcycle Diaries (film). The Motorcycle Diaries   …   Wikipedia

• Coherent sheaf — In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space …   Wikipedia

• Background and genesis of topos theory — This page gives some very general background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being abstruse. The level of abstraction involved cannot be reduced beyond a certain point; but on the… …   Wikipedia

• Injective sheaf — In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext .). There is a further group of related concepts applied to sheaves: flabby …   Wikipedia

• Constant sheaf — In mathematics, the constant sheaf on a topological space X associated to a set A is a sheaf of sets on X whose stalks are all equal to A. It is denoted by A or AX. The constant presheaf with value A is the presheaf that assigns to each open… …   Wikipedia