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.
Arithmetic localisation and completion of spectra
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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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The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring
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.