Recollements and tilting objects |
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Authors: | Lidia Angeleri Hü gel,Steffen Koenig |
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Affiliation: | a Dipartimento di Informatica, Settore Matematica, Università degli Studi di Verona, Strada Le Grazie 15 - Ca’ Vignal 2, I - 37134 Verona, Italyb Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany |
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Abstract: | We study connections between recollements of the derived category D(Mod R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature. Secondly, we show how to construct a recollement from a tilting module of projective dimension one. By Nicolás and Saorín (2009) [31], every recollement of D(Mod R) is associated to a differential graded homological epimorphism λ:R→S. We will focus on the case where λ is a homological ring epimorphism or even a universal localization. Our results will be employed in a forthcoming paper in order to investigate stratifications of D(Mod R). |
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Keywords: | 18E30 18E40 16D90 |
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