Weiletale motivic cohomology

General Introduction
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Search results
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Online References
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Paper References
Geisser: Weilétale motivic cohomology over finite fields (2004)
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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
arXiv:1007.1310 A generalization of the ArtinTate formula for fourfolds from arXiv Front: math.NT by Daichi Kohmoto We give a new formula for the special value at s=2 of the HasseWeil zeta function for smooth projective fourfolds under some assumptions (the Tate and Beilinson conjecture, finiteness of some cohomology groups, etc.). Our formula may be considered as a generalization of the ArtinTate(Milne) formula for smooth surfaces, and expresses the special zeta value almost exclusively in terms of inner geometric invariants such as higher Chow groups (motivic cohomology groups). Moreover we compare our formula with Geisser's formula for the same zeta value in terms of Weilétale motivic cohomology groups, and as a consequence (under additional assumptions) we obtain some presentations of weight two Weilétale motivic cohomology groups in terms of higher Chow groups and unramified cohomology groups.
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Other Information
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