{
  "id": "1906.07976",
  "version": "v1",
  "published": "2019-06-19T08:52:58.000Z",
  "updated": "2019-06-19T08:52:58.000Z",
  "title": "$n$-excisive functors, canonical connections, and line bundles on the Ran space",
  "authors": [
    "James Tao"
  ],
  "comment": "60 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth algebraic variety over $k$. We prove that any flat quasicoherent sheaf on $\\operatorname{Ran}(X)$ canonically acquires a D-module structure. In addition, we prove that, if the geometric fiber $X_{\\overline{k}}$ is connected and admits a smooth compactification, then any line bundle on $S \\times \\operatorname{Ran}(X)$ is pulled back from $S$, for any locally Noetherian $k$-scheme $S$. Both theorems rely on a family of results which state that the (partial) limit of an $n$-excisive functor defined on the category of pointed finite sets is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-19T08:52:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D24",
      "55R80"
    ],
    "keywords": [
      "line bundle",
      "excisive functor",
      "ran space",
      "canonical connections",
      "flat quasicoherent sheaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}