2016/05/31 by Frederik Marks, Jan Stovicek, Jan Št'ovíček
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Countable set #Morphism #Projective test #Quantum many-body systems #Set (abstract data type) #math.RA #math.RT #msc:16E30 #msc:16S85 #msc:18E40
paper · pdf · doi:10.1017/prm.2018.37
published as Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 511-532 · 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
openalex created_date 2016/06/24 · arxiv created 2017/01/28 · openalex publication_date 2018/12/27 · arxiv updated 2019/04/12 · openalex updated_date 2026/08/05
Abstract We show that silting modules are closely related with localizations of rings. More precisely, every partial silting module gives rise to a localization at a set of maps between countably generated projective modules and, conversely, every universal localization, 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.