CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES

Abstract The goal of this article is to extend the work Voevodsky and Morel on homotopy t -structure category motivic complexes context motives for logarithmic schemes. To do so, we prove an analogue Morel’s connectivity theorem show a purity statement $({\mathbf {P}}^1, \infty )$ -local sheaves with log transfers. ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ proved be compatible Voevodsky’s -structure; that is, comparison functor $R^{{\overline {\square }}}\omega ^*\colon {\operatorname {DM}^{eff}}}(k)\to -exact. heart Grothendieck abelian strictly cube-invariant transfers: use it build new version reciprocity in style Kahn-Saito-Yamazaki Rülling.