Minimal filtered free resolutions for analytic D-modules

Abstract

We define the notion of a minimal filtered free resolution for a filtered module over the ring D (h) , a homogenization of the ring D of analytic differential operators. This provides us with analytic invariants attached to a (bi)filtered D -module. We also give an effective argument using a generalization of the division theorem in D (h) due to Assi et al. (J. Pure. Appl. Algebra 164 (2001) 3–21), by which we obtain an upper bound for the length of minimal filtered resolutions.