with Charlotte Hardouin. C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 951--954


Combining the results in Hendriks (1996) [6], Di Vizio (2002) [1] and Di Vizio, Hardouin [2], we prove that the generic, algebraic or differential, Galois group of a q-difference modules over C{x} can always be characterized in terms of v-curvatures, in the spirit of the work of Katz (1982) [8]. We use this result to prove that the Malgrange–Granier D-groupoid of a linear q-difference system coincide, in a sense that we specify below, with a sort of Kolchin closure of the dynamics of the linear q-difference system and that the group that fixes a transversal, coincide with the differential generic Galois group.




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