Nilpotent invariant motives I

الأصل · EN

The purpose of this article is to clarify the question what makes motives A¹-homotopy invariance. we give construction of the stable model category of nilpotent invariant motives Motdgnilp and define the nilpotent invriant motives associated with schemes and relative exact categories. For a noetherian scheme X, there are two kind of motives associated with X in the homotopy category Ho(Motnilpdg), namely Mnilp(X) and Mnilp'(X). In general Mnilp(X) is not isomorphic to M'nilp(Xred). But there exists a canonical isomorphism Mnilp'(X)≃ Mnilp'(Xred) and if X is regular noetherian separated, M(X) is canonically isomorphic to M'(X).