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2020 On modules over motivic ring spectra
Elden Elmanto, Håkon Kolderup
Ann. K-Theory 5(2): 327-355 (2020). DOI: 10.2140/akt.2020.5.327

Abstract

We provide an axiomatic framework that characterizes the stable -categories that are module categories over a motivic spectrum. This is done by invoking Lurie’s -categorical version of the Barr–Beck theorem. As an application, this gives an alternative approach to Röndigs and Østvær’s theorem relating Voevodsky’s motives with modules over motivic cohomology and to Garkusha’s extension of Röndigs and Østvær’s result to general correspondence categories, including the category of Milnor–Witt correspondences in the sense of Calmès and Fasel. We also extend these comparison results to regular Noetherian schemes over a field (after inverting the residue characteristic), following the methods of Cisinski and Déglise.

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Elden Elmanto. Håkon Kolderup. "On modules over motivic ring spectra." Ann. K-Theory 5 (2) 327 - 355, 2020. https://doi.org/10.2140/akt.2020.5.327

Information

Received: 12 June 2019; Revised: 6 October 2019; Accepted: 22 October 2019; Published: 2020
First available in Project Euclid: 11 August 2020

zbMATH: 07224517
MathSciNet: MR4113773
Digital Object Identifier: 10.2140/akt.2020.5.327

Subjects:
Primary: 14F40, 14F42
Secondary: 19E15, 55P42, 55P43, 55U35

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.5 • No. 2 • 2020
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