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

Abstract

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

arXiv comment10 pages