Recollements and tilting objects
By Lidia Angeleri Hugel, S. Konig, Qunhua Liu. 2009
96 citations recorded by the source corpus.
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 Nicolas and Saorin (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 ).
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1d3df1369df5e2799e77d2328ac082011fb427a5
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In Algebra and Number Theory
- Oyvind Solberg
- Oystein Skartsaeterhagen
- Chrysostomos Psaroudakis
- Hongxing Chen
- Changchang Xi
- Yang Han
- Jiaqun Wei
- Osamu Iyama
In Geometry and Topology
- Oyvind Solberg
- Oystein Skartsaeterhagen
- Chrysostomos Psaroudakis
- Hongxing Chen
- Changchang Xi
- Yang Han
- Jiaqun Wei
- Osamu Iyama
Citations in the corpus
- Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements (2014, background): “Snashall and Solberg [59] have extended the theory of support varieties from group algebras to finite dimensional algebras by replacing the group cohomology H∗(G, k) with the Hochschild cohomology ring of the algebra.”
- Recollements and Hochschild theory (2011, background): “, all triangulated categories in the recollements are derived categories of algebras, which are closed related to tilting theory [1, 23, 32], (co)localization theory [31, 28], some important homological invariants of algebras such as global dimension [41, 22, 2], finitistic dimension [17], Hochschil”
- Good tilting modules and recollements of derived module categories (2010, background): “Infinite dimensional tilting theory has been of interest for a long time, but only recently it has increasingly attracted attention to understand derived categories of general rings and related topics (see [2, 4, 6, 7, 11, 12, 32]).”