Weight filtration of the limit mixed Hodge structure at infinity for tame polynomials

TL;DR

This paper provides three new proofs of a theorem relating the weight filtration and monodromy filtration of the limit mixed Hodge structure at infinity for cohomologically tame polynomials, clarifying their relationship.

Contribution

The paper introduces three novel proofs of Sabbah's theorem, enhancing understanding of the weight and monodromy filtrations in mixed Hodge structures for tame polynomials.

Findings

Weight filtration coincides with monodromy filtration up to a shift.

Three new proofs of Sabbah's theorem are provided.

Clarifies the relationship between filtrations in mixed Hodge structures.

Abstract

We give three new proofs of a theorem of C. Sabbah asserting that the weight filtration of the limit mixed Hodge structure at infinity of cohomologically tame polynomials coincides with the monodromy filtration up to a certain shift depending on the unipotent or non-unipotent monodromy part.