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Cellular objects in isotropic motivic categories

Fabio Tanania

Geometry & Topology 27 (2023) 2013–2048
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 –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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