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arXiv · 1207.0107

The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations

Jean-Pierre Ramis·Jacques Sauloy
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Abstract

In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem. In this paper, we completely describe the wild fundamental group and apply this result to the inverse problem in $q$-difference Galois theory. The new version contains an appendix on pronilpotent completion and the main result on the direct problem is made more precise. (Submitted for publication)

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BibTeXRIS

Jean-Pierre Ramis, Jacques Sauloy. 2012-11-29. The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations. https://arxiv.org/abs/1207.0107

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