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)