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

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