The Chow t-structure on the ∞-category of motivic spectra

• 成果类型: Article
• 署名作者: Bachmann, Tom; Kong, Hana Jia; Wang, Guozhen; Xu, Zhouli
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.2.5
• 发表日期: 2022
• 页码: 707-773
• 关键词: stable-homotopy; algebraic cobordism; steenrod algebra; COHOMOLOGY; OPERATIONS; stems

摘要

We define the Chow t-structure on the infinity-category of motivic spectra SH(k) over an arbitrary base field k. We identify the heart of this t-structure SH(k)(c(sic)) when the exponential characteristic of k is inverted. Restricting to the cellular subcategory, we identify the Chow heart SH(k)(cell,c(sic)) as the category of even graded MU2*MU-comodules. Furthermore, we show that the co-category of modules over the Chow truncated sphere spectrum 1(c=0) 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 infinity-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- Whitehead tower associated to the Chow t-structure and the motivic Adams spectral sequences over k.