Abelian varieties over Q with bad reduction in one prime only

(Un exposé de René Schoof au séminaire de théorie des nombres de Chevaleret le 28 novembre 2005)

Résumé :

  A classical theorem of Abrashkin/Fontaine states that there is no abelian variety over Q with good reduction everywhere. We will explain the proof of the following extension : For p at most 19, the only semi-stable abelian varieties over Q with good reduction everywhere except at p, are isogenous to a power of J_0(p)