{
  "id": "1211.6943",
  "version": "v1",
  "published": "2012-11-29T15:10:19.000Z",
  "updated": "2012-11-29T15:10:19.000Z",
  "title": "On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic",
  "authors": [
    "Damian Rössler"
  ],
  "categories": [
    "math.AG",
    "math.LO"
  ],
  "abstract": "Let $K$ be the function field of a smooth and proper curve $S$ over an algebraically closed field $k$ of characteristic $p>0$. Let $A$ be an ordinary abelian variety over $K$. Suppose that the N\\'eron model $\\CA$ of $A$ over $S$ has a closed fibre $\\CA_s$, which is an abelian variety of $p$-rank 0. We show that under these assumptions the group $A(K^\\perf)/\\Tr_{K|k}(A)(k)$ is finitely generated. Here $K^\\perf=K^{p^{-\\infty}}$ is the maximal purely inseparable extension of $K$. This result implies that in some circumstances, the \"full\" Mordell-Lang conjecture, as well as a conjecture of Esnault and Langer, are verified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-29T15:10:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K99"
    ],
    "keywords": [
      "function field",
      "purely inseparable points",
      "positive characteristic",
      "ordinary abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6943R"
    }
  }
}