| Résume | Given an integer N, we can naturally associate to each elliptic curveover Q a Galois representation mod N. Mazur asked if there existpairs of (non-isogenous) elliptic curves with isomorphic mod Nrepresentation. Using the geometry of a particular class of modularsurfaces introduced by Kani, which turns out to be a moduli space forMazur's problem, we prove that, for N=11, there are infinitely manysuch pairs (even if we cannot build a single example...) |
