Arithmetic localisation and completion of spectra
Algebraic Topology
2024-12-13 v1
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.
Cite
@article{arxiv.2412.09361,
title = {Arithmetic localisation and completion of spectra},
author = {Neil Strickland},
journal= {arXiv preprint arXiv:2412.09361},
year = {2024}
}