{
  "id": "1204.5979",
  "version": "v2",
  "published": "2012-04-26T16:41:17.000Z",
  "updated": "2012-05-20T18:56:53.000Z",
  "title": "Integration in algebraically closed valued fields with sections",
  "authors": [
    "Yimu Yin"
  ],
  "comment": "Minor revision in the last section",
  "categories": [
    "math.LO",
    "math.AG"
  ],
  "abstract": "We construct Hrushovski-Kazhdan style motivic integration in certain expansions of ACVF. Such an expansion is typically obtained by adding a full section or a cross-section from the RV-sort into the VF-sort and some (arbitrary) extra structure in the RV-sort. The construction of integration, that is, the inverse of the lifting map L, is rather straightforward. What is a bit surprising is that the kernel of L is still generated by one element, exactly as in the case of integration in ACVF. The overall construction is more or less parallel to the original Hrushovski-Kazhdan construction. As an application, we show uniform rationality of Igusa zeta functions for non-archimedean local fields with unbounded ramification degrees.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-20T18:56:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "11S80"
    ],
    "keywords": [
      "algebraically closed valued fields",
      "construct hrushovski-kazhdan style motivic integration",
      "non-archimedean local fields",
      "igusa zeta functions",
      "original hrushovski-kazhdan construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5979Y"
    }
  }
}