Arithmetic cohomology

General Introduction
Arithmetic cohomology can mean at least two things. The first is a notion of Geisser, who constructs a cohomology theory with compact supports for separated schemes of finite type over a finite field, which (assuming the Tate conjecture and rat=num) gives an integral model for ladic cohomology with compact supports when l is different from p. These groups are expected to be finitely generated and related to special values of zeta functions for all schemes as above. This is a variant of Weiletale cohomology, probably agreeing with it for smooth projective varieties, but being better behaved in general. For l=p his definition using the ehtopology gives a new theory which for smooth and proper schemes agrees with logarithmic de RhamWitt cohomology. See also Arithmetic homology
Arithmetic cohomology is also sometimes used as a synonym for Absolute cohomology. See also Absolute cohomology, Geometric cohomology
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Online References
Article of Nekovar
Arithmetic cohomology over finite fields and special values of zetafunctions, by Thomas Geisser
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Paper References
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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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