Cech cohomology

General Introduction
Under Sheaf cohomology we define Cech cohomology for an arbitrary Grothendieck topology.
This nLab entry compares derived functor sheaf cohomology with Cech cohomology: these two methods differ in whether one computes using “resolutions” of either the coefficient object A (this happens in the right derived global section functor approach) or in the domain object X (this happens in Čech cohomology).
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Online References
For the Cech nerve of a covering, see HuberWildeshaus app B.6
See the big paper of Thomason for spectra and stuff.
http://www.ncatlab.org/nlab/show/Cech+cohomology
Cech methods at the nLab, see also Cech homotopy, Cech cover, Cech nerve
http://www.ncatlab.org/nlab/show/Cech+model+structure+on+simplicial+presheaves
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Paper References
Hartshorne?
Bott and Tu?
Chapter 5 of Godement, in Homological algebra folder
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
http://mathoverflow.net/questions/9007/cechtoderivedspectralsequenceandsheafification
http://mathoverflow.net/questions/10056/equivalenceoforderedandunorderedcechcohomology
http://mathoverflow.net/questions/29737/understandcechcohomology
http://mathoverflow.net/questions/13977/istheresomethinglikecechcohomologyforpadicvarieties
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