de Mathématiques de Luminy
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.