Beschreibung:
AbstractThe goal of this article is to extend the work of Voevodsky and Morel on the homotopyt-structure on the category of motivic complexes to the context of motives for logarithmic schemes. To do so, we prove an analogue of Morel’s connectivity theorem and show a purity statement for$({\mathbf {P}}^1, \infty )$-local complexes of sheaves with log transfers. The homotopyt-structure on${\operatorname {\mathbf {logDM}^{eff}}}(k)$is proved to be compatible with Voevodsky’st-structure; that is, we show that the comparison functor$R^{{\overline {\square }}}\omega ^*\colon {\operatorname {\mathbf {DM}^{eff}}}(k)\to {\operatorname {\mathbf {logDM}^{eff}}}(k)$ist-exact. The heart of the homotopyt-structure on${\operatorname {\mathbf {logDM}^{eff}}}(k)$is the Grothendieck abelian category of strictly cube-invariant sheaves with log transfers: we use it to build a new version of the category of reciprocity sheaves in the style of Kahn-Saito-Yamazaki and Rülling.