CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES

CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES
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对数动机的连通性和纯度

DOI：
--
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发表时间：
2020
期刊：
Journal of the Institute of Mathematics of Jussieu
影响因子：
0.9
通讯作者：
Alberto Merici
Alberto Merici
中科院分区：
数学1区
文献类型：
--
作者：
F. Binda;Alberto Merici

文献摘要

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Abstract 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 $R^{{overline {square }}}omega ^*colon {operatorname {mathbf {DM}^{eff}}}(k) o {operatorname {mathbf {logDM}^{eff}}}(k)$ 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.
Abstract 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 $R^{{overline {square }}}omega ^*colon {operatorname {mathbf {DM}^{eff}}}(k) o {operatorname {mathbf {logDM}^{eff}}}(k)$ 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.