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...
10 KB (1,588 words) - 07:02, 11 November 2024
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...
68 KB (11,057 words) - 02:29, 4 December 2024
Ringed space (redirect from Structure sheaf)
{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...
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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...
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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...
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sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...
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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...
40 KB (6,934 words) - 06:32, 11 November 2024
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...
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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...
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Gluing axiom (redirect from B-sheaf)
In mathematics, the gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must...
10 KB (1,843 words) - 03:33, 5 November 2024
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...
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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...
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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 the local...
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Proj construction (redirect from Serre twist sheaf)
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...
19 KB (3,567 words) - 09:58, 30 July 2024
Differentiable manifold (redirect from Sheaf of smooth functions)
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...
67 KB (9,497 words) - 20:48, 13 December 2024
Inverse image functor (redirect from Inverse image sheaf)
image exhibits some relatively subtle features. Suppose we are given a sheaf G {\displaystyle {\mathcal {G}}} on Y {\displaystyle Y} and that we want...
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Direct image functor (redirect from Direct image of a sheaf)
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...
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Étale topology (redirect from Étale sheaf)
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...
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Locally constant function (category Sheaf theory)
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...
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Divisor (algebraic geometry) (redirect from Divisorial sheaf)
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...
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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...
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didukh (Ukrainian: дідух), is a Ukrainian Christmas decoration; made from a sheaf of wheat, it is a symbolic sacrifice taken from the autumn harvest. "Didukh"...
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Godement resolution (category Sheaf theory)
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...
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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...
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Stack Stalk is an outdoor 2001 sculpture by Ean Eldred and the architectural firm Rigga, located along the Eastbank Esplanade in Portland, Oregon. The...
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\operatorname {Spec} (R)} , that is, a prime ideal, then the stalk of the structure sheaf at p {\displaystyle {\mathfrak {p}}} equals the localization...
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(R_{j}/I_{j})} as schemes over U j {\displaystyle U_{j}} . There is a quasi-coherent sheaf of ideals I {\displaystyle {\mathcal {I}}} on X such that f ∗ O Z ≅ O X...
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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...
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Ringed topos (category Sheaf theory)
{\text{Open}}(X)} of a topological space X {\displaystyle X} , and the sheaf of continuous functions C X 0 : Open ( X ) o p → CRing {\displaystyle...
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Germ (mathematics) (category Sheaf theory)
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...
16 KB (2,684 words) - 01:26, 5 May 2024