Universal localisations via silting
arXiv:1605.04222 · doi:10.1017/prm.2018.37
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.
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
Cited by in corpus (6)
- Silting objects
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- Matlis category equivalences for a ring epimorphism
- Flat ring epimorphisms and universal localisations of commutative rings
- Zariski locality of quasi-coherent sheaves associated with tilting
- Flat commutative ring epimorphisms of almost Krull dimension zero