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Arithmetic localisation and completion of spectra

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arxiv 2412.09361 v1 pith:WM3Q5IUL submitted 2024-12-12 math.AT

Neil Strickland This is my paper · ORCID
classification math.AT
keywords p-completespectraspectrumhomologicalmodulesspherearithmeticbrown
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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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Cited by 1 Pith paper

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  1. The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring

    math.AC 2025-08 conditional novelty 7.0 of 10

    The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring is described by a distributive lattice of asymptotic growth classes of monotone integer sequences.

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