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

Abstract

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 characteristic cycle formula for lattices of regular holonomic $${\mathscr {D}}$$ -modules following ideas of Sabbah and Briancon–Maisonobe–Merle, and (2) the constructibility of the log de Rham complexes for lattices of holonomic $${\mathscr {D}}$$ -modules, which is a natural generalization of Kashiwara’s constructibility theorem.