{
  "id": "2001.07229",
  "version": "v1",
  "published": "2020-01-20T19:37:54.000Z",
  "updated": "2020-01-20T19:37:54.000Z",
  "title": "A Bound for the Image Conductor of a Principally Polarized Abelian Variety with Open Galois Image",
  "authors": [
    "Jacob Mayle"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be a principally polarized abelian variety of dimension $g$ over a number field $K$. Assume that the image of the adelic Galois representation of $A$ is open. Then there exists a positive integer $m$ so that the Galois image of $A$ is the full preimage of its reduction modulo $m$. The least $m$ with this property, denoted $m_A$, is called the image conductor of $A$. A recent paper (arXiv:1904.10431) established an upper bound for $m_A$, in terms of standard invariants of $A$, in the case that $A$ is an elliptic curve without complex multiplication. In this note, we generalize the aforementioned result to provide an analogous bound in arbitrary dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-20T19:37:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principally polarized abelian variety",
      "open galois image",
      "image conductor",
      "adelic galois representation",
      "complex multiplication"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}