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

Yuki Mifune; Ryo Takahashi

doi:10.2969/jmsj/92709270

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

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

Yuki Mifune, Ryo Takahashi

著者情報

キーワード: derived category, Verdier quotient, singularity category, additive generator, punctured spectrum, maximal Cohen–Macaulay module, finite/countable CM type, hypersurface, simple singularity

ジャーナル認証あり

2025 年 77 巻 2 号 p. 563-579

DOI https://doi.org/10.2969/jmsj/92709270

詳細

抄録

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.