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arXiv · 1405.5090

Recollements of derived categories III: finitistic dimensions

Hongxing Chen·Changchang Xi
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Abstract

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.

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Hongxing Chen, Changchang Xi. 2014-05-20. Recollements of derived categories III: finitistic dimensions. https://arxiv.org/abs/1405.5090

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