Almost mathematics of pointed symmetric monoidal model categories by Smith ideal theory
Abstract
This article is a generalization of a result in Quillen's note ``Module theory over non-unital rings'' giving a one-to-one correspondence between bilocalization of abelian categories of modules and idempotent ideals of the base ring. Faltings; Gabber and Ramero established almost mathematics, the same as Quillen's bilocalization of a category of modules by nil modules. In this paper, by using the theory of Smith ideals mentioned in Hovey and Smith, we consider almost mathematics of symmetric monoidal pointed model categories. We prove a weak analogue of the one-to-one correspondence in Quillen.
Keywords
Cite
@article{arxiv.2301.04541,
title = {Almost mathematics of pointed symmetric monoidal model categories by Smith ideal theory},
author = {Yuki Kato},
journal= {arXiv preprint arXiv:2301.04541},
year = {2026}
}
Comments
Corresponds to the version submitted for publication. Added an example on derived torsion and derived completion; clarified the relation to related independent work. Main results unchanged