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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• Search results

  MathSciNet

  Google Scholar

  Google

  arXiv: Experimental full text search

  arXiv: Abstract search

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• Online References

  For the Cech nerve of a covering, see Huber-Wildeshaus 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

  http://mathoverflow.net/questions/78065/long-exact-sequence-for-cech-cohomology

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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/4214/equivalence-of-grothendieck-style-versus-cech-style-sheaf-cohomology

  http://mathoverflow.net/questions/78439/ordered-cech-like-complexes-that-compute-etale-cohomology-of-fields

  http://mathoverflow.net/questions/19312/when-does-cech-cohomology-fail-to-be-the-same-as-derived-functor-cohomology

  http://mathoverflow.net/questions/60888/can-we-relate-cech-cohomology-and-derived-functor-cohomology-even-when-the-cover

  http://mathoverflow.net/questions/9007/cech-to-derived-spectral-sequence-and-sheafification

  http://mathoverflow.net/questions/10056/equivalence-of-ordered-and-unordered-cech-cohomology

  http://mathoverflow.net/questions/29737/understand-cech-cohomology

  http://mathoverflow.net/questions/13977/is-there-something-like-cech-cohomology-for-p-adic-varieties

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• Comments Posted

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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments