On Ramis's solution of the local inverse problem of differential Galois theory. - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 1994

On Ramis's solution of the local inverse problem of differential Galois theory.

Claude Mitschi
  • Fonction : Auteur
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Michael F. Singer
  • Fonction : Auteur

Résumé

Recently, J.P. Ramis gave necessary and sufficient conditions for a linear algebraic group to be the Galois group of a Picard-Vessiot extension of the field ${\bf C}\{x\}[x^{-1}]$ of germs of meromorphic functions at zero. The conditions of Ramis are stated in terms of the Lie algebra of the group. In this paper, we give equivalent simple group theoretic conditions, and show how these generalize previous conditions of Kovacic in the solvable case.
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hal-00129711 , version 1 (08-02-2007)

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  • HAL Id : hal-00129711 , version 1

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Claude Mitschi, Michael F. Singer. On Ramis's solution of the local inverse problem of differential Galois theory.. 1994. ⟨hal-00129711⟩
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