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Qu'est-ce (qui) est quasicoherent sheaf - définition

FINITE-TYPE SHEAF F OF MODULES OVER A RINGED SPACE SUCH THAT THE KERNEL OF A SURJECTIVE MORPHISM FROM A FINITE DIRECT SUM OF THE STRUCTURE SHEAF ONTO IT IS ALSO OF FINITE TYPE

Coherent sheaves; Holomorphic sheaf; Quasi-coherent; Quasi-coherent sheaves; Quasicoherent sheaf; Quasicoherent; Quasi-coherent sheaf; Locally free sheaf; Locally free sheaves; Vector bundle over a ringed space; Coherent analytic sheaf; Quasi-coherent module; Algebraic vector bundle; Draft:Locally free sheaf and an algebraic vector bundle; Algebraic bundle; Resolution property; Vector bundle (algebraic geometry)

Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information.

https://en.wikipedia.org/wiki/Coherent_sheaf

sheaf

WIKIMEDIA DISAMBIGUATION PAGE

Sheaf (disambiguation)

(sheaves)

1.

A sheaf of papers is a number of them held or fastened together.

He took out a sheaf of papers and leafed through them.

N-COUNT: usu N of n

2.

A sheaf of corn or wheat is a number of corn or wheat plants that have been cut down and tied together.

N-COUNT

sheaf

WIKIMEDIA DISAMBIGUATION PAGE

Sheaf (disambiguation)

¦ noun (plural sheaves)

1. a bundle of grain stalks laid lengthways and tied together after reaping.

2. a bundle of objects, especially papers.

¦ verb bundle into sheaves.

Origin

OE sceaf, of Gmc origin; related to shove.

Wikipédia

Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information.

Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under operations such as taking kernels, images, and cokernels. The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free sheaves of infinite rank.

Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf.

https://en.wikipedia.org/wiki/Coherent sheaf