Divisibility of zeta functions of curves in a covering

Yves Aubry (1, 2) , Marc Perret (3)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme
3 ENS de Lyon - École normale supérieure de Lyon

As an analogous of a conjecture of Artin, we show that, if $ Y\longrightarrow 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 ${\sb Z}[T]$. We give some interpretations of this result in terms of semi-abelian varieties.

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Marc Perret. Divisibility of zeta functions of curves in a covering. Archiv der Mathematik, 2004, 82, pp.205--213. ⟨hal-00978051⟩