Singular equivalences of commutative noetherian rings and reconstruction of singular loci

Abstract

Two left noetherian rings $R$ and $S$ are said to be {\it singularly equivalent} if their singularity categories are equivalent as triangulated categories. The aim of this paper is to give a necessary condition for two commutative noetherian rings to be singularly equivalent. To do this, we develop the support theory for triangulated categories without tensor structure.

21 pages, Title is changed, Section 5 is added, minor changes

References in corpus (1)

• Local rings with quasi-decomposable maximal ideal

Cited by in corpus (1)

• Construction of spectra of triangulated categories without tensor structure and applications to commutative rings