The Irregularity of the Direct Image of Some $\mathcal D$-modules

Abstract

Let f and g be two regular functions on U smooth affne variety. Let \mathcal M be a regular holonomic \mathcal D_U -module. We are interested in the irregularity of the complex f_+(\mathcal Me^g) . More precisely, we relate the irregularity number at c of the systems \mathcal H^kf_+(\mathcal Me^g) with the characteristic cycles of the systems \mathcal H^k(f, g)_+(\mathcal M) .