论文标题
对数动机的连通性和纯度
Connectivity and Purity for logarithmic motives
论文作者
论文摘要
本文的目的是将Voevodsky和Morel在动机综合体类别的同型$ t $结构上的工作扩展到对数方案的动机背景。为此，我们证明了Morel连接定理的类似物，并显示了$（\ Mathbf {p}^1，\ infty）$的纯度语句 - 带有日志传输的沿束带的局部复合体。 $ \ mathbf {logdm}^{\ textrm {fextrm {fef}}（k）$在$ \ mathbf {logdm}上的同型$ t $ - 结构被证明与voevodsky的$ t $结构兼容。 \ Mathbf {dm}^{\ textrm {eff}}}（k）\ to \ mathbf {logdm}^{\ textrm {eff}}}（k）$是$ t $ -exact。 $ \ mathbf {logdm}^{\ textrm {fextrm {fextrm {eff}}（k）$是$ \ mathbf {logdm}^{$ t $结构的核心是严格的立方体式吊床的Grothendieck Abelian类别：我们使用它来构建它的新版本，以构建新版本的回报和kah sheaiv and kah and kah sheav and k k.ah syn sy sy s of n of k.卢林。
The goal of this paper 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 $\mathbf{logDM}^{\textrm{eff}}(k)$ is proved to be compatible with Voevodsky's $t$-structure i.e. we show that the comparison functor $R^{\overline{\square}}ω^*\colon \mathbf{DM}^{\textrm{eff}}(k)\to \mathbf{logDM}^{\textrm{eff}}(k)$ is $t$-exact. The heart of the homotopy $t$-structure on $\mathbf{logDM}^{\textrm{eff}}(k)$ 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.
