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arXiv · 1611.00535

Relative derived dimensions for cotilting modules

Michio Yoshiwaki
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Abstract

For a Noetherian ring $R$ and a cotilting $R$-module $T$ of injective dimension at least $1$, we prove that the derived dimension of $R$ with respect to the category $\mathcal{X}_T$ is precisely the injective dimension of $T$ by applying Auslander-Buchweitz theory and Ghost Lemma. In particular, when $R$ is a commutative Noetherian local ring with a canonical module $\omega_R$ and $\dim R\ge1$, the derived dimension of R with respect to the category of maximal Cohen-Macaulay modules is precisely $\dim R$.

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Michio Yoshiwaki. 2016-11-02. Relative derived dimensions for cotilting modules. https://arxiv.org/abs/1611.00535

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