Location of Repository

J1(p) Has Connected Fibers

By Brian Conrad, Bas Edixhoven and William Stein

Abstract

We study resolution of tame cyclic quotient singularities on arithmetic surfaces, and use it to prove that for any subgroup H ⊆ (Z/pZ) × /{±1} the map XH(p) = X1(p)/H → X0(p) induces an injection Φ(JH(p)) → Φ(J0(p)) on mod p component groups, with image equal to that of H in Φ(J0(p)) when the latter is viewed as a quotient of the cyclic group (Z/pZ) × /{±1}. In particular, Φ(JH(p)) is always Eisenstein in the sense of Mazur and Ribet, and Φ(J1(p)) is trivial: that is, J1(p) has connected fibers. We also compute tables o

Topics: Jacobians of modular curves, Component groups, Resolution of singularities Contents
Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.190.8974
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://math.stanford.edu/%7Eco... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.