Coverings of singular curves over finite fields

Yves Aubry (1) , Marc Perret (2)

1 IML - Institut de mathématiques de Luminy
2 ENS de Lyon - École normale supérieure de Lyon

We prove that if $f : Y\longrightarrow X$ is a finite fiat morphism between two reduced absolutely irreducible algebraic projective curves defined over the finite field ${\sb F}_q$, then $$\mid \sharp Y({\sb F}_q) - \sharp X({\sb F}_q)\mid \leq 2({\pi}_Y - {\pi}_X)\sqrt q,$$ where $\pi_C$ is the arithmetic genus of a curve $C$. As application, we give some character sum estimation on singular curves.

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Marc Perret. Coverings of singular curves over finite fields. Manuscripta mathematica, 1995, 88 (1), pp.467--478. ⟨10.1007/BF02567835⟩. ⟨hal-00976489⟩