Aubry Yves and Perret Marc.
Divisibility of zeta functions of curves in a covering.

As an analogous of a conjecture of Artin, we show that, if Y
—› X is a finite flat morphism between two singular
reduced absolutely irreducible projective algebraic curves defined over
a finite field, then the numerator polynomial of the zeta function of
X divides those of Y in Z[T]. We give some interpretations
of this result in terms of semi-abelian varieties.