Minimal filtered free resolutions for analytic D-modules

AbstractWe 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