English

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.

Keywords

Cite

@article{arxiv.2412.09361,
  title  = {Arithmetic localisation and completion of spectra},
  author = {Neil Strickland},
  journal= {arXiv preprint arXiv:2412.09361},
  year   = {2024}
}
R2 v1 2026-06-28T20:32:37.158Z