Recollements of derived categories III: finitistic dimensions

In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely related to a longstanding conjecture, the finitistic dimension con...

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Bibliographic Details
Published inarXiv.org
Main Authors Chen, Hongxing, Changchang Xi
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.05.2014
Subjects
Algebra
Homology
Rings (mathematics)
Sequences
Upper bounds
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Summary:In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely related to a longstanding conjecture, the finitistic dimension conjecture, in representation theory and homological algebra. Further, we apply our results to a series of situations of particular interest: exact contexts, ring extensions, trivial extensions, pullbacks of rings, and algebras induced from Auslander-Reiten sequences. In particular, we not only extend and amplify Happel's reduction techniques for finitistic dimenson conjecture to more general contexts, but also generalise some recent results in the literature.
ISSN:2331-8422