On some curve singularity invariants and reductions

Abstract

This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta function of the curve by means of motivic integration over a suitable ring of ad\'eles, whose reduction modulo a maximal ideal will coincide with some already known zeta functions of the singularity.