The goal of this article is to extend the work of Voevodsky and Morel on the homotopy t-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 homotopy t-structure on ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ is proved to be compatible with Voevodsky’s t-structure; that is, we show that the comparison functor $R^{{\overline {\square }}}\omega ^*\colon {\operatorname {\mathbf {DM}^{eff}}}(k)\to {\operatorname {\mathbf {logDM}^{eff}}}(k)$ is t-exact. The heart of the homotopy t-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.

本文的目的是将 Voevodsky 和 ​​Morel在动机复合体类别上的同伦t结构的工作扩展到对数方案的动机背景。为此，我们证明了莫雷尔连通性定理的类比，并展示了 $({\mathbf {P}}^1, \infty )$ - 具有对数传递的层的局部复合体的纯度声明。 ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ 上的同伦t结构被证明与 Voevodsky 的t结构兼容；也就是说，我们证明比较函子 $R^{{\overline {\square }}}\omega ^*\colon {\operatorname {\mathbf {DM}^{eff}}}(k)\to {\ operatorname {\mathbf {logDM}^{eff}}}(k)$ 是t -精确的。 ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ 上的同伦t结构的核心是具有对数传递的严格立方不变层的 Grothendieck 阿贝尔范畴：我们用它来构建一个Kahn-Saito-Yamazaki 和 Rülling 风格的互惠滑轮类别的新版本。