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

Bachmann, Tom; Kong, Hana Jia; Wang, Guozhen und Xu, Zhouli (2022): The Chow t-structure on the infinity-category of motivic spectra. In: Annals of Mathematics, Bd. 195, Nr. 2: S. 707-773

Abstract

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0003-486X
• Sprache: Englisch