{
  "id": "2004.04089",
  "version": "v1",
  "published": "2020-04-08T16:12:54.000Z",
  "updated": "2020-04-08T16:12:54.000Z",
  "title": "Etale triviality of finite vector bundles over compact complex manifolds",
  "authors": [
    "Indranil BIswas"
  ],
  "comment": "Final version",
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "A vector bundle $E$ over a projective variety $M$ is called finite if it satisfies a nontrivial polynomial equation with nonnegative integral coefficients. Introducing finite bundles, Nori proved that $E$ is finite if and only if the pullback of $E$ to some finite \\'etale covering of $M$ is trivializable \\cite{No1}. The definition of finite bundles extends naturally to holomorphic vector bundles over compact complex manifolds. We prove that a holomorphic vector bundle over a compact complex manifold $M$ is finite if and only if the pullback of $E$ to some finite \\'etale covering of $M$ is holomorphically trivializable. Therefore, $E$ is finite if and only if it admits a flat holomorphic connection with finite monodromy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-08T16:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32L10",
      "53C55",
      "14D21"
    ],
    "keywords": [
      "compact complex manifold",
      "finite vector bundles",
      "etale triviality",
      "holomorphic vector bundle",
      "finite etale covering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}