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CONFLUENTES MATHEMATICI

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Galois theories of q-difference equations: comparison theorems
Lucia Di Vizio1 ; Charlotte Hardouin2
1 Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France
2 Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 11-35.

We establish some comparison results among the different parameterized Galois theories for q-difference equations, completing the work [4], that addresses the problem in the case without parameters. Our main result is the link between the abstract parameterized Galois theories, that give information on the differential properties of abstract solutions of q-difference equations, and the properties of meromorphic solutions of such equations. Notice that a linear q-difference equation with meromorphic coefficients always admits a basis of meromorphic solutions, as proven in [25].

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DOI : 10.5802/cml.66
Classification : 39A13, 12H10
Mots clés : Galois group; $q$-difference equations; differential Tannakian categories; Kolchin differential groups.
Lucia Di Vizio 1 ; Charlotte Hardouin 2

1 Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France
2 Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Lucia Di Vizio; Charlotte Hardouin. Galois theories of $q$-difference equations: comparison theorems. Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 11-35. doi : 10.5802/cml.66. https://cml.centre-mersenne.org/articles/10.5802/cml.66/

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