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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 ...

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, ...

Coherent sheaf - Encyclopedia of Mathematics

www.encyclopediaofmath.org/index.php/Coherent_sheaf

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 ...

algebraic geometry - Is skyscraper sheaf quasi-coherent ...

math.stackexchange.com/questions/642262/is-skyscraper-sheaf-quasi-coherent

Jan 18, 2014 ... Suppose F is a skyscraper sheaf supported on { p } ¯ , the stalk is M , What is its global section over Spec ⁡ A ? We need to find a module N ...

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 ...

Rank, degree and slope of a general coherent sheaf - Mathematics ...

math.stackexchange.com/questions/895086/rank-degree-and-slope-of-a-general-coherent-sheaf

Aug 12, 2014 ... Let ( X , O X ) be a ringed space and F be a coherent sheaf of O X -modules on ( X , O X ) . Are there the definitions of rank, degree and slope of ...

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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 ...

Coherent Sheaves - Mit

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 ...

The cohomology of coherent sheaves - Penn Math

www.math.upenn.edu

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 ...