{
  "id": "1602.06237",
  "version": "v1",
  "published": "2016-02-19T17:54:50.000Z",
  "updated": "2016-02-19T17:54:50.000Z",
  "title": "Abelian varieties isogenous to a power of an elliptic curve",
  "authors": [
    "Bruce W. Jordan",
    "Allan G. Keeton",
    "Bjorn Poonen",
    "Eric M. Rains",
    "Nicholas Shepherd-Barron",
    "John T. Tate"
  ],
  "comment": "21 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve over a field $k$. Let $R:= \\text{End}\\, E$. There is a functor $\\mathscr{H}\\!\\!\\mathit{om}_R(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a power of $E$, and a functor $\\text{Hom}(-,E)$ in the opposite direction. We prove necessary and sufficient conditions on $E$ for these functors to be equivalences of categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-19T17:54:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian varieties isogenous",
      "elliptic curve",
      "opposite direction",
      "torsion-free left",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160206237J"
    }
  }
}