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Universal localizations via silting

Published online by Cambridge University Press:  27 December 2018

Frederik Marks
Affiliation:
University of Stuttgart, Institute for Algebra and Number Theory, Pfaffenwaldring 57, 70569 Stuttgart, Germany ([email protected])
Jan Št'ovíček
Affiliation:
Faculty of Mathematics and Physics, Department of Algebra, Charles University in Prague, Sokolovská 83, 186 75 Praha, Czech Republic ([email protected])

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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