On Ramis's solution of the local inverse problem of differential Galois theory.
Mitschi, Claude ; Singer, Michael F.
HAL, hal-00129711 / Harvested from HAL
Text on HAL
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.
Publié le : 1994-11-02
Classification:  Differential Galois theory,  Inverse problem in Galois theory,  "Differential Galois theory,  Linear algebraic groups,  Inverse problem in Galois theory.",  12H05, 20G99, 12F12,  [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] 
@article{hal-00129711,
     author = {Mitschi, Claude and Singer, Michael F.},
     title = {On Ramis's solution of the local inverse problem of differential Galois theory.},
     journal = {HAL},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129711}
}

Mitschi, Claude; Singer, Michael F. On Ramis's solution of the local inverse problem of differential Galois theory.. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129711/