Institut
de Mathématiques de Luminy

Abstract 2003-07 |

**Aubry** Yves, **Perret** Marc.

On the characteristic polynomials of the Frobenius endomorphism for projective
curves over finite fields

We give a formula for the number of rational
points of projective algebraic curves defined over a finite field, and
a bound "à la Weil" for connected ones. More precisely, we give
the characteristic polynomials of the Frobenius endomorphism on the
étale -adic
cohomology groups of the curve. Finally, as an analogue of Artin's holomorphy
conjecture, we prove that, if Y —> X is a finite flat morphism
between two varieties over a finite field, then the characteristic polynomial
of the Frobenius morphism on H |