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## Coherent sheaf - Wikipedia

en.wikipedia.org/wiki/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 ...

## coherent sheaf in nLab

ncatlab.org/nlab/show/coherent sheaf

Jun 2, 2014 ... 1. Idea. A coherent sheaf of modules is a geometric globalization of the notion of coherent module. 2. Definition. Over a ringed topos. Let ( X , �� ) ...

## quasicoherent sheaf in nLab

ncatlab.org/nlab/show/quasicoherent sheaf

5 days ago ... A quasicoherent sheaf of modules (often just “quasicoherent sheaf”, for short) is a sheaf of modules over the structure sheaf of a ringed space ...

## Stacks Project — Tag 029N: Quasi-coherent Sheaves

stacks.math.columbia.edu/tag/029N

Quasi-coherent Sheaves. Definition 92.35.1. Let be a scheme. A sheaf of - modules is quasi-coherent if for every affine open the restriction is of the form for some ...

## Stacks Project — Tag 01XY: Coherent sheaves on locally ...

stacks.math.columbia.edu/tag/01XY

Although it is possible to consider coherent sheaves on non-Noetherian schemes we will always assume the base scheme is locally Noetherian when we ...

## Stacks Project — Tag 01Y7: Coherent sheaves on Noetherian ...

stacks.math.columbia.edu/tag/01Y7

Lemma 29.10.2. Let be a Noetherian scheme. Let be a coherent sheaf on . Let be a quasi-coherent sheaf of ideals corresponding to a closed subscheme .

## ag.algebraic geometry - Do I know what "coherent sheaf" means if I ...

mathoverflow.net/questions/206077/do-i-know-what-coherent-sheaf-means-if-i-know-what-it-means-on-locally-noether

May 8, 2015 ... I've been trying to convince myself that "coherent sheaf" is a natural definition. One way I might be satisfied is the following: for modules over a ...

## algebraic geometry - Why did Serre choose coherent sheaves ...

math.stackexchange.com/questions/1400481/why-did-serre-choose-coherent-sheaves

Aug 17, 2015 ... First thing - I don't know any algebraic geometry. I'm trying to understand a little bit about quasi-coherent sheaves but not for the sake of AG, ...

## CoherentSheaf -- the class of all coherent sheaves

www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.9/share/doc/Macaulay2/Macaulay2Doc/html/___Coherent__Sheaf.html

Functions and methods returning a coherent sheaf : ambient(CoherentSheaf) ( missing documentation); CoherentSheaf ** CoherentSheaf -- tensor produce of ...

## 4. Coherent Sheaves Definition 4.1. If (X,O X) is a locally ringed ...

math.mit.edu/~mckernan/Teaching/09-10/Spring/18.726/l_4.pdf

Coherent Sheaves. Definition 4.1. If (X,OX) is a locally ringed space, then we say that an OX-module F is locally free if there is an open affine cover {Ui} of X such ...