Formal structure of direct image of holonomic D-modules of exponential type

TL;DR

This paper investigates the formal invariants of cohomology sheaves from direct images of holonomic D-modules of exponential type, establishing a classification result after ramification.

Contribution

It provides a computation of formal invariants and proves an isomorphism classification for formal modules as direct images of exponential type D-modules.

Findings

Computed formal invariants for cohomology sheaves.

Proved isomorphism of formal modules to direct images after ramification.

Established classification results for formal D-modules of exponential type.

Abstract

We compute formal invariants associated with the cohomology sheaves of the direct image of holonomic D-modules of exponential type. We also prove that every formal C[[t]]<\partial_t>-modules is isomorphic, after a ramification, to a germ of formalized direct image of analytic D-module of exponential type.