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Recollements and tilting objects
Authors:Lidia Angeleri Hü  gel,Steffen Koenig
Affiliation:
  • a Dipartimento di Informatica, Settore Matematica, Università degli Studi di Verona, Strada Le Grazie 15 - Ca’ Vignal 2, I - 37134 Verona, Italy
  • b Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
  • 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:RS. 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).
    Keywords:18E30   18E40   16D90
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