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arXiv · 2403.07725

Algebraicity in monochromatic homotopy theory

Torgeir Aambø
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Abstract

Using Patchkoria--Pstr\k{a}gowski'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 $\mathrm{Sp}_{K_p(n)}$ of Barthel--Schlank--Stapleton.

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Torgeir Aambø. 2024-03-12. Algebraicity in monochromatic homotopy theory. https://doi.org/10.2140/agt.2025.25.5665

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