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-Tate motives DATM(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. Exactness properties of these functors familiar from perverse sheaves are shown to hold in this context. The cohomological dimension of mixed Artin-Tate motives (MATM(S)) is two, and there is an equivalence DATM(S)≅Db(MATM(S)). © 2010 Elsevier B.V.
Mixed Artin-Tate motives over number rings
Scholbach J.
2011
Abstract
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-Tate motives DATM(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. Exactness properties of these functors familiar from perverse sheaves are shown to hold in this context. The cohomological dimension of mixed Artin-Tate motives (MATM(S)) is two, and there is an equivalence DATM(S)≅Db(MATM(S)). © 2010 Elsevier B.V.
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