Cellular objects in isotropic motivic categories

Tanania, Fabio

doi:10.2140/gt.2023.27.2013

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Cellular objects in isotropic motivic categories

Fabio Tanania

Geometry & Topology 27 (2023) 2013–2048

DOI: 10.2140/gt.2023.27.2013

Abstract

Our main purpose is to describe the category of isotropic cellular spectra over flexible fields. Guided by Gheorghe, Wang and Xu (Acta Math. 226 (2021) 319–407), we show that it is equivalent, as a stable $\infty$ –category equipped with a $t$ –structure, to the derived category of left comodules over the dual of the classical topological Steenrod algebra. In order to obtain this result, the category of isotropic cellular modules over the motivic Brown–Peterson spectrum is also studied, and isotropic Adams and Adams–Novikov spectral sequences are developed. As a consequence, we also compute hom sets in the category of isotropic Tate motives between motives of isotropic cellular spectra.

Keywords

motivic homotopy theory, isotropic motivic categories, Steenrod algebra, Adams spectral sequences

Mathematical Subject Classification

Primary: 14F42

References

Publication

Received: 12 March 2021

Revised: 6 December 2021

Accepted: 15 January 2022

Published: 27 July 2023

Proposed: Jesper Grodal

Seconded: Marc Levine, Stefan Schwede

Authors

Fabio Tanania
Mathematisches Institut Ludwig-Maximilians-Universität München Munich Germany

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Volume 27, issue 5 (2023)