The Balmer spectrum of a tame stack

Abstract

Let $X$ be a quasicompact algebraic stack with quasifinite and separated diagonal. We classify the thick $\otimes$-ideals of ${\mathsf{D}}_{\text{ qc}}{\left(X\right)}^c$. 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 $X_{\text{ cs}}$, then we prove that the Balmer spectra of $X$ and $X_{\text{ cs}}$ are naturally isomorphic.