D\'ecomposition en \'el\'ements simples des formes m\'eromorphes formelles ferm\'ees

TL;DR

This paper proves that closed formal meromorphic 1-forms can be decomposed into simple elements, enabling a generalized notion of residue that extends classical concepts to formal settings.

Contribution

It introduces a partial fraction decomposition for closed formal meromorphic 1-forms and extends the residue concept to this formal context.

Findings

Existence of a partial fraction decomposition for closed formal meromorphic 1-forms

Extension of the residue notion to formal meromorphic forms

Framework for analyzing formal meromorphic forms using classical tools

Abstract

We show that any closed formal meromorphic 1-form admits a "partial fraction decomposition", which allows us in particular to define a notion of residue for closed formal meromorphic forms which extends the notion defined for usual forms.