The Poincaré series of a simple complete ideal of a two-dimensional regular local ring

Abstract

The aim of this work is to introduce both a classical and a motivic Poincaré series associated with a residually rational simple complete m -primary ideal ℘ of a two-dimensional regular local ring ( R , m ) . We describe them in terms of the generators of the value semigroup of ℘ , and compare them with the Poincaré series arising from a general element f for ℘ .