Algebraicity in monochromatic homotopy theory

Aambø, Torgeir

doi:10.2140/agt.2025.25.5665

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Algebraicity in monochromatic homotopy theory

Torgeir Aambø

Algebraic & Geometric Topology 25 (2025) 5665–5692

DOI: 10.2140/agt.2025.25.5665

Abstract

Using Patchkoria and Pstrągowski’s version of Franke’s algebraicity theorem, we prove that the category of $K_{p} (n)$ -local spectra is exotically equivalent to the category of derived $I_{n}$ -complete periodic comodules over the Adams Hopf algebroid $(E_{*}, E_{*} E)$ for large primes. This gives a finite prime result analogous to the asymptotic algebraicity for ${Sp}_{K_{p} (n)}$ of Barthel, Schlank, and Stapleton.

Keywords

algebraic models, chromatic homotopy theory, monochromatic spectra, local duality, comodules, Hopf algebroids, torsion

Mathematical Subject Classification

Primary: 55N35, 55P42, 55P60

References

Publication

Received: 22 April 2024

Revised: 14 October 2024

Accepted: 3 December 2024

Published: 18 December 2025

Authors

Torgeir Aambø
Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim Norway

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Volume 25, issue 9 (2025)