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Stokes phenomenon, multisummability and differential Galois groups

Michèle Loday-Richaud — 1994

Annales de l'institut Fourier

We precise the cohomological analysis of the Stokes phenomenon for linear differential systems due to Malgrange and Sibuya by making a rigid natural choice of a unique cocycle (called a Stokes cocyle) in every cohomological class. And we detail an algebraic algorithm to reduce any cocycle to its cohomologous Stokes form. This gives rise to an almost algebraic definition of sums for formal solutions of systems which we compare to the most usual ones. We also use this construction to the Stokes cocycle...

On index theorems for linear ordinary differential operators

Michèle Loday-Richaud;  Geneviève Pourcin — 1997

Annales de l'institut Fourier

We introduce and study the sheaf of Deligne to describe singular points of a linear differential operator D and we develop a technique based on homological algebra to prove index theorems for D . As particular cases, we obtain index theorems for D acting in spaces of multisummable series and a new proof of the index theorem of Malgrange in the space of convergent power series and of the index theorems of Ramis in the spaces of Gevrey series. We compute the values of these...

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