Characteristic cycles associated to holonomic $\mathcal{D}$-modules

We study relative and logarithmic characteristic cycles associated to holonomic $\mathcal{D}$-modules. As applications, we obtain: (1) an alternative proof of Ginsburg’s log characteristic cycle formula for lattices of regular holonomic $\mathcal{D}$-modules following ideas of Sabbah and Briancon-Maisonobe-Merle, and (2) the constructibility of the log de Rham complexes for lattices of holonomic $\mathcal{D}$-modules, which is a natural generalization of Kashiwara’s constructibility theorem.