with Charlotte Hardouin. Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 11-35. 
ABSTRACT:
We establish some comparison results among the different Galois theories, parameterized or not, for q-difference equations, completing the work of Chatzidakis-Hardouin-Singer. 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.
DOI : https://doi.org/10.5802/cml.66
ArXiv: 1205.1696
HAL: hal-00794745