fcohomology

General Introduction
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Search results
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Online References
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Paper References
Greenlees and May: Generalized Tate cohomology (book)
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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:1003.1219 fcohomology and motives over number rings from arXiv Front: math.AG by Jakob Scholbach This paper is concerned with an interpretation of fcohomology, a modification of motivic cohomology of motives over number fields, in terms of motives over number rings. Under standard assumptions on mixed motives over finite fields, number fields and number rings, we show that the two extant definitions of fcohomology of mixed motives $M\eta$ over Fone via ramification conditions on $\ell$adic realizations, another one via the Ktheory of proper regular modelsboth agree with motivic cohomology of $\eta{!} M\eta[1]$. Here $\eta{!}$ is constructed by a limiting process in terms of intermediate extension functors $j_{!*}$ defined in analogy to perverse sheaves.
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Other Information
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