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arXiv · 2408.12206

Upper bounds for dimensions of singularity categories and their annihilators

Souvik Dey·Yuki Mifune
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Abstract

Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules and by $\operatorname{D^b}(R)$ the bounded derived category of $\operatorname{mod} R$. In this paper, we first investigate localizations and annihilators of Verdier quotients of $\operatorname{D^b}(R)$. After that, we explore upper bounds for the dimension of the singularity category of $R$ and its (strong) generators. We extend a theorem of Liu to the case where $R$ is neither an isolated singularity nor even a local ring. Some of our results are more generally stated in terms of Spanier--Whitehead category of a resolving subcategory.

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Souvik Dey, Yuki Mifune. 2024-08-22. Upper bounds for dimensions of singularity categories and their annihilators. https://arxiv.org/abs/2408.12206

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