coherent sheaf (Q1839)

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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

Language	Label	Description	Also known as
English	coherent sheaf	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

Statements

quasicoherent sheaf

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discoverer or inventor

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Fragments of the history of sheaf theory

16

defining formula

\left(\forall (U,n)\exists ({\mathcal {O}}_{U}^{n}\to {\mathcal {F}}\to 0)\right)\land \left(\forall ({\mathcal {O}}_{U}^{n}{\xrightarrow {\phi }}{\mathcal {F}}_{U}\to 0)\exists ({\mathcal {O}}_{U}^{m}\to \ker \phi \to 0)\right)

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1940s

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Identifiers

/m/02vmcd

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Freebase Data Dumps

publication date

28 October 2013

coherent sheaf

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Microsoft Academic ID

143161588

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C143161588

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26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

CoherentSheaf

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Encyclopedia of Mathematics article ID

Coherent_sheaf

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Sitelinks

mathematics(0 entries)

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