Zariski cohomology

General Introduction
By Zariski cohomology we mean Sheaf cohomology of some sheaf (or complex of sheaves) on the Zariski site of a scheme.The sheaf can be for example a coherent sheaf as in Hartshorne, or a motivic complex as in Voevodsky.
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Online References
A very nice introduction by Daniel Murfet.
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Paper References
Hartshorne: Algebraic geometry
EMS Vol 35 (Alg geom II), ed Shafarevich. Covers cohomology of coherent sheaves and etale cohomology. In Cohomology folder under AG.
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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
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