Fractional ideals and integration with respect to the generalised Euler characteristic

Abstract

Let b be a fractional ideal of a one-dimensional Cohen-Macaulay local ring O containing a perfect field k. This paper is devoted to the study some O-modules associated with b. In addition, different motivic Poincaré series are introduced by considering ideal filtrations associated with b; the corresponding functional equations of these Poincaré series are also described.