Fractional ideals and integration with respect to the generalised Euler characteristic

Abstract

Let bb be a fractional ideal of a one-dimensional Cohen–Macaulay local ring containing a perfect field. This paper is devoted to the study of the motivic Poincaré series defined by different filtrations associated with bb in the form of Euler integrals with respect to the generalised Euler characteristic; in particular, the functional equations of the Poincaré series are also described.