English

The Left Localization Principle, completions, and cofree $G$-spectra

Algebraic Topology 2021-03-16 v3 Commutative Algebra

Abstract

We show under mild hypotheses that a Quillen adjunction between stable model categories induces another Quillen adjunction between their left localizations, and we provide conditions under which the localized adjunction is a Quillen equivalence. Moreover, we show that in many cases the induced Quillen equivalence is symmetric monoidal. Using our results we construct a symmetric monoidal algebraic model for rational cofree GG-spectra. In the process, we also show that LL-complete modules provide an abelian model for derived complete modules.

Keywords

Cite

@article{arxiv.1910.01410,
  title  = {The Left Localization Principle, completions, and cofree $G$-spectra},
  author = {Luca Pol and Jordan Williamson},
  journal= {arXiv preprint arXiv:1910.01410},
  year   = {2021}
}

Comments

Revised version, to appear in J. Pure Appl. Algebra. v3: corrigendum added as an appendix, together with footnotes in the main body directing the reader to the corrigendum where necessary