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

TL;DR

This paper investigates characteristic cycles of holonomic D-modules, providing new proofs of existing formulas and establishing constructibility results for log de Rham complexes, advancing understanding in algebraic analysis.

Contribution

It offers an alternative proof of Ginsburg's log characteristic cycle formula and proves the constructibility of log de Rham complexes for holonomic D-modules.

Findings

Alternative proof of Ginsburg's formula

Constructibility of log de Rham complexes

Generalization of Kashiwara's theorem

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.