Mixed Artin–Tate motives over number rings

AbstractThis 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))