The Balmer spectrum of a tame stack

Abstract

Let $X$ be a quasi-compact algebraic stack with quasi-finite and separated diagonal. We classify the thick $\otimes$-ideals of ${\mathsf{D}}_{\mathrm{qc}}(X{)}^c$. If $X$ is tame, then we also compute the Balmer spectrum of the $\otimes$-triangulated category of perfect complexes on $X$. In addition, if $X$ admits a coarse space $X_{\mathrm{cs}}$, then we prove that the Balmer spectra of $X$ and $X_{\mathrm{cs}}$ are naturally isomorphic.

Cited by in corpus (4)

• Perfect complexes on algebraic stacks
• Geometricity for derived categories of algebraic stacks
• The telescope conjecture for algebraic stacks
• Addendum: Étale dévissage, descent and pushouts of stacks