SMF

Serre's conjecture on Galois represenations attached to Weil curves with additive reduction

Serre's conjecture on Galois represenations attached to Weil curves with additive reduction

Joan-C. LARIO
  • Année : 1992
  • Tome : 209
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 11F70
  • Pages : 246-255
  • DOI : 10.24033/ast.169

In a joint work with P. Bayer [Ba-La 91], we verify Serre's conjecture (3.2.4$_?$) (in Duke J.) for the Galois representation defined by the $p$-torsion points of $p$-vertical Weil curves. In this paper our purpose is to emphasize the difference between the $p$-vertical and the $p$-horizontal cases in order to check Serre's conjecture. Several numerical examples, collected by computer calculations, lead us to give a conjecture which implies (3.2.4$_?$) for the horizontal case.

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