{
  "id": "1411.6295",
  "version": "v1",
  "published": "2014-11-23T20:42:33.000Z",
  "updated": "2014-11-23T20:42:33.000Z",
  "title": "The Balmer spectrum of a tame stack",
  "authors": [
    "Jack Hall"
  ],
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-23T20:42:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "13D09",
      "14A20",
      "18G10"
    ],
    "keywords": [
      "balmer spectrum",
      "tame stack",
      "quasi-compact algebraic stack",
      "coarse space",
      "perfect complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6295H"
    }
  }
}