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 𝖣^𝖻(𝑅) the bounded derived category of finitely generated 𝑅-modules. In this paper, we study the structure of the Verdier quotient 𝖣^𝖻(𝑅)/𝗍𝗁𝗂𝖼𝗄(𝑅 ⊕ 𝑘). We give necessary and sufficient conditions for it to admit an additive generator.