Propagation of the Irregularity of a Microdifferential System

Abstract

We construct the functor of microlocal analytic irregularity $I\mu \mathrm{hom}(\cdot ,{\mathcal{O}}_X)$ which gives a natural third term of a distinguished triangle associated to the transformation $t_{\mu }\mathrm{hom}(\cdot ,{\mathcal{O}}_X)\to \mu \mathrm{hom}(\cdot ,{\mathcal{O}}_X)$ of functors on the derived category of $R$-constructible sheaves. When restricting to $C$-constructible objects we prove that the microlocal irregularity of a microdifferential system propagates along non 1-microcharacteristic directions, as a consequence of the propagation for $t\mu \mathrm{hom}(\cdot ,{\mathcal{O}}_X)$ and $\mu \mathrm{hom}(\cdot ,{\mathcal{O}}_X$).