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Faltings in 1983 proved that a necessary and sufficient condition for twoabelian varieties $A$ and $B$ to be isogenous over a number field $K$ is thatthe local factors of the L-series of $A$ and $B$ are equal for almost allprimes of $K$ ; for each such prime this implies that $A$ and $B$ have the samenumber of points over the residue field. We show in this article that forabelian varieties faithfully of type GSp (a class containing the abelianvarieties with endomorphism ring $\mathbb{Z}$ and of odd dimension) `having thesame number of points' may be replaced by `the number of points have the sameprime divisors' and still gives a sufficient condition for $A$ and $B$ to be$K$-isogenous. The proof is based on ideas of Serre \cite{serreim72} andFrey-Jarden \cite{FJ} and follows closely Hall-Perucca \cite{hallp} who provedthe result for elliptic curves.

Classe d'isog\'enie de vari\'et\'es ab\'eliennes pleinement de type GSp