Cellular objects in isotropic motivic categories

Tanania, Fabio¹

¹ Mathematisches Institut, Ludwig-Maximilians-Universität München, Munich, Germany

Geometry & topology, Tome 27 (2023) no. 5, pp. 2013-2048.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.2013

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

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