Publications of the Research Institute for Mathematical Sciences


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Volume 50, Issue 3, 2014, pp. 457–476
DOI: 10.4171/PRIMS/140

Published online: 2014-09-17

La Construction d’Abbes et Saito pour les Connexions Méromorphes: Aspect Formel en Dimension 1

Jean-Baptiste Teyssier[1]

(1) Freie Universität Berlin, Germany

In [AS09], Abbes and 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 $\mathcal{M}$.

Keywords: Differential modules, Levelt–Turrittin polynomials, nearby cycles.

Teyssier Jean-Baptiste: La Construction d’Abbes et Saito pour les Connexions Méromorphes: Aspect Formel en Dimension 1. Publ. Res. Inst. Math. Sci. 50 (2014), 457-476. doi: 10.4171/PRIMS/140