In mathematics, the stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open...

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...

axes of a vascular plant Pituitary stalk, a part of the brain Stalk (sheaf), a mathematical construction The Stalk, a 1994 science fiction novel by Chris...

{O}}_{X}} to be the sheaf of real-valued (or complex-valued) continuous functions on open subsets of X {\displaystyle X} . The stalk at a point 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...

spirit: a coherent sheaf F {\displaystyle {\mathcal {F}}} on a scheme X {\displaystyle X} is a vector bundle if and only if its stalk F x {\displaystyle...

constant sheaf on a topological space X {\displaystyle X} associated to a set A {\displaystyle A} is a sheaf of sets on X {\displaystyle X} whose stalks are...

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...

algebraic topology, the orientation sheaf on a manifold X of dimension n is a locally constant sheaf oX on X such that the stalk of oX at a point x is o X , x...

S_{1}} is a coherent sheaf and locally generates S over S 0 {\displaystyle S_{0}} (that is, when we pass to the stalk of the sheaf S at a point x of X...

image exhibits some relatively subtle features. Suppose we are given a sheaf G {\displaystyle {\mathcal {G}}} on Y {\displaystyle Y} and that we want...

of OX (defined stalk-wise, or on open affine charts). For a morphism f: X → Y and a closed subscheme Y′ ⊆ Y defined by an ideal sheaf J, the preimage...

In mathematics, the gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must...

exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry. Let M be a complex manifold, and write OM for the sheaf of...

In the Zariski topology, the stalk of X at x is computed by taking a direct limit of the sections of the structure sheaf over all the Zariski open neighborhoods...

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...

In mathematics, the direct image functor is a construction in sheaf theory that generalizes the global sections functor to the relative case. It is of...

differentiable functions on U. As U varies, this determines a sheaf of rings on Rn. The stalk Op for p ∈ Rn consists of germs of functions near p, and is...

then verify that the sheaf axioms hold for this construction, giving us a sheaf of abelian groups (even commutative rings). This sheaf could be written Z...

effective Cartier divisor on X is an ideal sheaf I which is invertible and such that for every point x in X, the stalk Ix is principal. It is equivalent to...

the sheaf in terms of local information coming from its stalks. It is useful for computing sheaf cohomology. It was discovered by Roger Godement. Given...

group scheme G on a scheme X over a base scheme S, an equivariant sheaf F on X is a sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules together with...

The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical...

\operatorname {Spec} (R)} , that is, a prime ideal, then the stalk of the structure sheaf at P equals the localization of R at the ideal P, and this is...

that formation of stalks preserves finite limits. This implies that if T is a Lawvere theory and a sheaf F is a T-algebra, then any stalk Fx is also a T-algebra...

space factors through r. An analytic space is normal if every stalk of the structure sheaf is a normal ring (meaning an integrally closed integral domain)...

M} . If F is a quasicoherent sheaf on a scheme X, the support of F is the set of all points x in X such that the stalk Fx is nonzero. This definition...

Stack Stalk is an outdoor 2001 sculpture by Ean Eldred and the architectural firm Rigga, located along the Eastbank Esplanade in Portland, Oregon. The...

the 'fiftieth day' of the count. The omer ("sheaf") is an old Biblical measure of volume of unthreshed stalks of grain, the amount of grain used for the...

_{X\setminus X_{n-2}}} is the constant sheaf on X ∖ X n − 2 {\displaystyle X\setminus X_{n-2}} . By replacing the constant sheaf on X ∖ X n − 2 {\displaystyle...