Universal localisations via silting
Abstract
We show that silting modules are closely related with localisations of rings. More precisely, every partial silting module gives rise to a localisation at a set of maps between countably generated projective modules and, conversely, every universal localisation, in the sense of Cohn and Schofield, arises in this way. To establish these results, we further explore the finite-type classification of tilting classes and we use the morphism category to translate silting modules into tilting objects. In particular, we prove that silting modules are of finite type.
Cite
@article{arxiv.1605.04222,
title = {Universal localisations via silting},
author = {Frederik Marks and Jan Stovicek},
journal= {arXiv preprint arXiv:1605.04222},
year = {2019}
}
Comments
20 pages; version 2: Subsection 6.4 added with an example of a silting ring epimorphism which is not a universal localisation, small changes in presentation (e.g. Proposition 3.3 now summarizes properties of set-generated cotorsion pairs), references added and updated