{
  "id": "1806.09168",
  "version": "v1",
  "published": "2018-06-24T15:46:13.000Z",
  "updated": "2018-06-24T15:46:13.000Z",
  "title": "Log smoothness and polystability over valuation rings",
  "authors": [
    "Karim Adiprasito",
    "Gaku Liu",
    "Igor Pak",
    "Michael Temkin"
  ],
  "comment": "38 pages, first version, comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\mathcal{O}$ be a valuation ring of height one of residual characteristic exponent $p$ and with algebraically closed field of fractions. Our main result provides a best possible resolution of the monoidal structure $M_X$ of a log variety $X$ over $\\mathcal{O}$: there exists a log modification $Y\\to X$ such that the monoidal structure of $Y$ is polystable. In particular, if $X$ is log smooth over $\\mathcal{O}$ then $Y$ is polystable. As a corollary we deduce that any log variety over $\\mathcal{O}$ possesses a polystable alteration of degreee $p^n$. The core of our proof is a subdivision result for polyhedral complexes satisfying certain rationality conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-24T15:46:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "valuation ring",
      "log smoothness",
      "polystability",
      "log variety",
      "monoidal structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}