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arXiv · 1411.6295

The Balmer spectrum of a tame stack

Jack Hall
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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.

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Jack Hall. 2014-11-23. The Balmer spectrum of a tame stack. https://doi.org/10.2140/akt.2016.1.259

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