A remark on the irregularity complex

TL;DR

This paper proves that for certain meromorphic flat bundles, the irregularity complex's restriction to each stratum depends only on the formal bundle, addressing a question by Teyssier.

Contribution

It establishes a dependence result for irregularity complexes on formal flat bundles along strata, clarifying their local behavior.

Findings

Irregularity complex restriction depends only on formal flat bundle

Addresses a question by Teyssier

Includes correction from published erratum

Abstract

We prove that, for a good meromorphic flat bundle with poles along a divisor with normal crossings, the restriction of the irregularity complex to each natural stratum of this divisor only depends on the formal flat bundle along this stratum. This answers a question raised by J.-B. Teyssier. This version takes into account the published erratum.