f-cohomology and motives over number rings
نویسندگان
چکیده
منابع مشابه
-cohomology and Motives over Number Rings
This paper is concerned with an interpretation of f -cohomology, 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 f -cohomology of mixed motives Mh over a number field F—one via ramification condition...
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This paper studies Artin–Tate motives over bases S ⊂ Spec OF , for a number field F . As a subcategory of motives over S, the triangulated category of Artin–TatemotivesDATM(S) is generated by motives φ∗1(n), where φ is any finite map. After establishing the stability of these subcategories under pullback and pushforward along open and closed immersions, a motivic t-structure is constructed. Exa...
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Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein rings. This paper improves the theory further by giving a new definition that works over more general rings, specifically, those with a dualizing complex. The new definition of Tate cohomology retains the desirable prop...
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Article history: Received 26 April 2007 Communicated by Michel Van Den Bergh
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We prove that if M , N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of Ext R (M,N) for n ≫ 0 is equivalent to the vanishing of Ext R (N,M) for n ≫ 0. Furthermore, if b R has no embedded deformation, then such vanishing occurs if and only if M or N has finite projective dimension.
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 2012
ISSN: 0386-5991
DOI: 10.2996/kmj/1333027252