Absolute cohomology

General Introduction
In nature, some cohomology theories in algebraic geometry seem to come in pairs, where one cohomology is referred to as "absolute" (or "arithmetic") and the other is referred to as "geometric". This is explained in section 3 of Nekovar's survey article on the Beilinson conjectures (available here as well as in Motives vol I).
Examples of absolute cohomology theories should include Continuous etale cohomology, Absolute Hodge cohomology, Syntomic cohomology, and Motivic cohomology?
See also Arithmetic cohomology, Geometric cohomology
Remark: The term "absolute cohomology" was sometimes used back in the 80s for what we today call motivic cohomology.
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Search results
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Online References
Nekovar's survey on the Beilinson conjectures (see section 3)
In Toën's AIM talk on Homotopy types of algebraic varieties, there is a homotopical approach to the absolute/geometric dichotomy. File available here
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Paper References
Jannsen: LNM 1400 (Mixed motives and algebraic Ktheory).
See reading notes from André, chapter 14.
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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
There might be a vague intuitive idea saying that Deninger's conjectural cohomology should be the geometric theory corresponding to the absolute theory which is Weiletale cohomology. One could also ask if Arakelov motivic cohomology could be viewed as an absolute theory and if so, what is the corresponding geometric 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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Comments Posted
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