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Coherent sheaf

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 ...

quasicoherent sheaf in nLab

ncatlab.org/nlab/show/quasicoherent sheaf

May 1, 2016 ... A quasicoherent sheaf of modules (often just “quasicoherent sheaf”, for short) is a sheaf of modules over the structure sheaf of a ringed space ...

Sheaves of Modules - Stacks Project

stacks.math.columbia.edu/download/modules.pdf

11. Modules of finite presentation. 13. 12. Coherent modules. 15. 13. Closed immersions of ringed spaces. 17. 14. Locally free sheaves. 19. 15. Tensor product.

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 ...

A quasi-coherent sheaf of notes

amathew.files.wordpress.com/2010/07/031.pdf

A quasi-coherent sheaf of notes. Akhil Mathew. July 25, 2010. Abstract. These are a bunch of notes taken to help myself learn algebraic geom- etry. My main ...

The cohomology of coherent sheaves - Penn Math

www.math.upenn.edu/~chai/624_08/mumford-oda_chap7-8.pdf

The cohomology of coherent sheaves. 1. Basic Cech cohomology. We begin with the general set-up. (i) X any topological space. U = {Uα}α∈S an open covering ...

Coherent analytic sheaf - Encyclopedia of Mathematics

www.encyclopediaofmath.org/index.php/Coherent_analytic_sheaf

Aug 22, 2014 ... A coherent sheaf of O modules on an analytic space ( X , O ) . A space ( X , O ) is said to be coherent if O is a coherent sheaf of rings.

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, ...

algebraic geometry - When is the sheaf corresponding to a vector ...

math.stackexchange.com/questions/198558/when-is-the-sheaf-corresponding-to-a-vector-bundle-on-a-smooth-manifold-coherent

Sep 18, 2012 ... They are in particular examples of quasi-coherent sheaves. If the bundle is of finite rank, then the sheaf is actually coherent and this is good for ...

“A variety is completely recovered by its category of coherent ...

math.rice.edu/~jrc9/stuff/posterpeloso.pdf

coherent sheaves.” Let's be more precise: Theorem (Gabriel) Let X,Y be two varieties, then X is isomorphic to Y if and only if the category Coh(X) is equivalent to ...

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coherent sheaf in nLab

ncatlab.org

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

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

math.mit.edu

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 ...

Coherent sheaf - Encyclopedia of Mathematics

www.encyclopediaofmath.org

Nov 24, 2013 ... A coherent sheaf on a ringed space ( X , O ) is a sheaf of modules F over a sheaf of rings O with the following properties: 1) F is a sheaf of finite ...