The construction of Abbes and Saito for meromorphic connections: formal aspects of dimension 1 (Q473123)

Summary: In [ibid. 45, No. 1, 25--74 (2009; Zbl 1225.11151)], \textit{A. Abbes} and \textit{T. Saito} define a measure of wild ramification of \(\ell\)-adique sheaves at a generic point of a complete trait of characteristic \(p\), with \(p\neq \ell\). Adapting their construction to differential modules of characteristic zero, we show for such a module \(\mathcal{M}\) a formula which expresses that geometric invariant in terms of differential forms appearing in the Levelt-Turrittin decomposition of \(\mathcal{M}\).