{
  "id": "1211.6684",
  "version": "v2",
  "published": "2012-11-28T18:00:58.000Z",
  "updated": "2013-10-29T16:37:30.000Z",
  "title": "Overconvergent subanalytic subsets in the framework of Berkovich spaces",
  "authors": [
    "Florent Martin"
  ],
  "comment": "Some points of the presentation have been changed, more details are given, but there are no new results",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We study the class of overconvergent subanalytic subsets of a $k$-affinoid space $X$ when $k$ is a non-archimedean field. These are the images along the projection $X \\times B^n \\to X$ of subsets defined with inequalities between functions of $X\\times B^n$ which are overconvergent in the variables of $B^n$. In particular, we study the local nature, with respect to $X$, of overconvergent subanalytic subsets. We show that they behave well with respect to the Berkovich topology, but not to the $G$-topology. This gives counter-examples to previous results on the subject, and a way to correct them. Moreover, we study the case dim$(X)=2$, for which a simpler characterisation of overconvergent subanalytic subsets is proven.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-29T16:37:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G22"
    ],
    "keywords": [
      "overconvergent subanalytic subsets",
      "berkovich spaces",
      "non-archimedean field",
      "simpler characterisation",
      "local nature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6684M"
    }
  }
}