Calcul d’indices et irrégularité pour les systèmes holonomes. (French) Zbl 0569.58031

Systèmes différentiels et singularités, Colloq. Luminy/France 1983, Astérisque 130, 352-364 (1985).
[For the entire collection see Zbl 0559.00004.]
The author gives a short account of a forthcoming paper. He states an index theorem for the formal series solutions of a holonomic differential system belonging to Gevrey classes \({\mathbb{C}}[[ x]]_{(r)}\), \(1\leq r\leq \infty\). This includes as special cases results previously obtained by J. P. Ramis [Astérisque 59/60, 173-204 (1978; Zbl 0409.34018)] and by M. Kashiwara [Systems of microdifferential equations, Progr. Math. 34 (1983; Zbl 0521.58057)]. The latter is recommended as a reference for the necessary background.
Reviewer: H.Schröder


58J20 Index theory and related fixed-point theorems on manifolds