论文标题
$ \ infty $ - 动机光谱类别上的chow $ t $结构
The Chow $t$-structure on the $\infty$-category of motivic spectra
论文作者
论文摘要
我们在任意基本场上$ k $上定义了$ \ infty $ spation $ sh（k）$的$ \ infty $ - 类别上的chow $ t $ t $结构。当$ k $的指数特征被倒置时，我们确定了此$ t $ structure $ sh（k）^{c \ heartsuit} $的核心。限制在蜂窝子类别中，我们将Chow Heart $ SH（k）^{cell，c \ heartsuit} $作为均匀分级$ mu_ {2*} mu $ $ -odules的类别。此外，我们证明了chow截断的球形频谱上的$ \ infty $ - 模块的类别是代数。 我们的结果在三个方面概括了Gheorghe-Wang-XU中的结果：积分结果；除了仅$ c $以外的所有基地；对于整个$ \ infty $ - 动机光谱$ sh（k）$的类别，而不是仅包含某些蜂窝对象的子类别。 我们还讨论了一种使用与Chow $ t $结构相关的Postnikov Tower和$ k $的动机Adams光谱序列相关的尼科夫塔的计算动机稳定同型组（p完整的）球体（p填充）球体的策略。
We define the Chow $t$-structure on the $\infty$-category of motivic spectra $SH(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $SH(k)^{c\heartsuit}$ when the exponential characteristic of $k$ is inverted. Restricting to the cellular subcategory, we identify the Chow heart $SH(k)^{cell, c\heartsuit}$ as the category of even graded $MU_{2*}MU$-comodules. Furthermore, we show that the $\infty$-category of modules over the Chow truncated sphere spectrum is algebraic. Our results generalize the ones in Gheorghe--Wang--Xu in three aspects: To integral results; To all base fields other than just $C$; To the entire $\infty$-category of motivic spectra $SH(k)$, rather than a subcategory containing only certain cellular objects. We also discuss a strategy for computing motivic stable homotopy groups of (p-completed) spheres over an arbitrary base field $k$ using the Postnikov tower associated to the Chow $t$-structure and the motivic Adams spectral sequences over $k$.
