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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 ...

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.

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 , �� ) ...

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 ...

FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 31

math.stanford.edu/~vakil/0708-216/216class31.pdf

Feb 6, 2008 ... Coherent sheaves don't always push forward to coherent sheaves. For example ... a coherent sheaf on X, show that f∗F is a coherent sheaf.

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, ...

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 ...

CHAPTER VII The cohomology of coherent sheaves

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.

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 ...

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

stacks.math.columbia.edu

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

quasicoherent sheaf in nLab

ncatlab.org

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 ...

ag.algebraic geometry - is the category of coherent sheaves some ...

mathoverflow.net

Nov 27, 2013 ... On a reasonably nice, at least noetherian, scheme (or variety, algebraic space, stack), can the category of coherent sheaves be constructed ...