{
  "id": "0805.1916",
  "version": "v3",
  "published": "2008-05-13T19:56:25.000Z",
  "updated": "2009-03-11T18:45:45.000Z",
  "title": "Analytification is the limit of all tropicalizations",
  "authors": [
    "Sam Payne"
  ],
  "comment": "13 pages. v3: expository improvements throughout, especially in section 5 on fields with the trivial valuation. added appendix showing that tropicalization is invariant under extensions of valued fields",
  "journal": "Math. Res. Lett. 16 (2009), no. 3, 543--556",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce extended tropicalizations for closed subvarieties of toric varieties and show that the analytification of a quasprojective variety over a nonarchimedean field is naturally homeomorphic to the inverse limit of the tropicalizations of its quasiprojective embeddings.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-03-11T18:45:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32C99",
      "14G22"
    ],
    "keywords": [
      "analytification",
      "inverse limit",
      "nonarchimedean field",
      "toric varieties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1916P"
    }
  }
}