Smashing localizations of rings of weak global dimension at most one

We show for a ring R of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in R. If, moreover, R is commutative, we prove that the compactly generated localizing subca...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-01, Vol.305, p.351-401
Main Authors: Bazzoni, Silvana, Šťovíček, Jan
Format: Article
Language:English
Subjects:
Homological epimorphism
Smashing localization
Telescope Conjecture
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Summary:We show for a ring R of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in R. If, moreover, R is commutative, we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms. We also classify smashing localizations of the derived category of any valuation domain, and provide an easy criterion for the Telescope Conjecture (TC) for any commutative ring of weak global dimension at most one. As a consequence, we show that the TC holds for any commutative von Neumann regular ring R, and it holds precisely for those Prüfer domains which are strongly discrete.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.09.028