On a Verdier quotient of a derived category of a local ring

Yuki Mifune; Ryo Takahashi

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arXiv · 2312.13544

On a Verdier quotient of a derived category of a local ring

Yuki Mifune·Ryo Takahashi

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Abstract

Let $R$ be a commutative noetherian local ring with residue field $k$. Denote by $\mathsf{D^b}(R)$ the bounded derived category of finitely generated $R$-modules. In this paper, we study the structure of the Verdier quotient $\mathsf{D^b}(R)/\mathsf{thick}(R\oplus k)$. We give necessary and sufficient conditions for it to admit an additive generator.

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Yuki Mifune, Ryo Takahashi. 2023-12-21. On a Verdier quotient of a derived category of a local ring. https://arxiv.org/abs/2312.13544

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