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Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian...

mathematics, the constant sheaf on a topological space X {\displaystyle X} associated to a set A {\displaystyle A} is a sheaf of sets on X {\displaystyle...

sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...

restrictions. Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the...

gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must satisfy, given that...

geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric...

of a scheme with respect to a coherent sheaf of ideals. Projective space Algebraic geometry of projective spaces Projectivization Ravi Vakil (2015). Foundations...

properties. A perverse sheaf is an object C of the bounded derived category of sheaves with constructible cohomology on a space X such that the set of...

In mathematics, an invertible sheaf is a sheaf on a ringed space that has an inverse with respect to tensor product of sheaves of modules. It is the equivalent...

Topological module Topological abelian group Properly discontinuous Sheaf space Topology glossary List of topology topics List of geometric topology...

analytic sheaf on a complex analytic space, and an analogous notion of a coherent algebraic sheaf on a scheme. In both cases, the given space X {\displaystyle...

In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module...

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...

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...

underlying topological space X {\displaystyle X} consists of points. It is reasonable to attempt to isolate the behavior of a sheaf at a single fixed point...

that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions...

\mapsto t_{X}\circ \varphi } for each coherent sheaf F on X (the superscript * refers to a dual vector space). The linear functional t X {\displaystyle t_{X}}...

same space X, the kernel of f is an ideal sheaf in A. Conversely, for any ideal sheaf J in a sheaf of rings A, there is a natural structure of a sheaf of...

therefore, is a sheaf on the topological space, called the "structure sheaf". On each open subset of the topological space, the sheaf specifies a collection...

sheaf of holomorphic functions (thus arriving at the spaces of complex analytic geometry), or the sheaf of polynomials (thus arriving at the spaces of...