Cellular objects in isotropic motivic categories

TL;DR

This paper characterizes the category of isotropic cellular spectra over flexible fields, showing its equivalence to a derived category of comodules over the dual Steenrod algebra, and develops spectral sequences for computations.

Contribution

It establishes an equivalence between isotropic cellular spectra and a derived category of comodules, and introduces spectral sequences for motivic computations.

Findings

Equivalence of isotropic cellular spectra to derived category of comodules

Development of isotropic Adams and Adams-Novikov spectral sequences

Computation of hom sets in isotropic Tate motives

Abstract

Our main purpose is to describe the category of isotropic cellular spectra over flexible fields. Guided by [6], 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.