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arXiv · 2412.09361

Arithmetic localisation and completion of spectra

Neil Strickland
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Abstract

This is an exposition of facts about p-local spectra, p-complete spectra and modules over the p-complete sphere spectrum, including homological criteria for finiteness. Most things are well-known to the experts, with a couple of potential exceptions: every dualisable p-complete spectrum is the p-completion of a finite spectrum, and the category of modules over the p-complete sphere has homological Brown representability.

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Neil Strickland. 2024-12-12. Arithmetic localisation and completion of spectra. https://arxiv.org/abs/2412.09361

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