Zeta functions and Cartier divisors on singular curves over finite fields (Q1383235)

The author studies the zeta functions associated with effective Cartier divisors on geometrically integral complete curves \(X\), defined over a finite field \(k\), with possible singularities. He studies the relationship between the local factors at a singular point \(Q \in X\) and the semigroup of values associated with the local ring \({\mathcal O}_Q\). For \(k\) large enough it is shown that the local factors at \(Q\) are determined by the semigroup of values associated with \({\mathcal O}_Q\).