{
  "id": "math/0103203",
  "version": "v2",
  "published": "2001-03-28T21:31:25.000Z",
  "updated": "2002-09-08T15:49:44.000Z",
  "title": "The endomorphism rings of jacobians of cyclic covers of the projective line",
  "authors": [
    "Yuri G. Zarhin"
  ],
  "comment": "LaTeX2e, 14 pages. The paper will appear in Math. Proc. Cambridge Philos. Soc",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Suppose K is a field of characteristic 0, $K_a$ is its algebraic closure, p is an odd prime. Suppose, $f(x) \\in K[x]$ is a polynomial of degree $n \\ge 5$ without multiple roots. Let us consider a curve $C: y^p=f(x)$ and its jacobian J(C). It is known that the ring End(J(C)) of all $K_a$-endomorphisms of J(C) contains the ring $Z[\\zeta_p]$ of integers in the pth cyclotomic field (generated by obvious automorphisms of C). We prove that $End(J(C))=Z[\\zeta_p]$ if the Galois group of f over K is either the symmetric group $S_n$ or the alternating group $A_n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-09-08T15:49:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14K15",
      "14C25"
    ],
    "keywords": [
      "cyclic covers",
      "endomorphism rings",
      "projective line",
      "pth cyclotomic field",
      "multiple roots"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......3203Z"
    }
  }
}