2012/05/08 by Lucia Di Vizio, Di Vizio, Lucia, Charlotte Hardouin +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #12H99 #39A13 #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Polynomial and algebraic computation #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1205.1694
openalex publication_date 2012/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We introduce the parameterized generic Galois group of a q-difference module, that is a differential group in the sense of Kolchin. It is associated to the smallest differential tannakian category generated by the q-difference module, equipped with the forgetful functor. Our previous results on the Grothendieck conjecture for q-difference equations lead to an adelic description of the parameterized generic Galois group, in the spirit of the Grothendieck-Katz's conjecture on p-curvatures. Using this description, we show that the Malgrange-Granier D-groupoid of a nonlinear q-difference system coincides, in the linear case, with the parameterized generic Galois group introduced here. The paper is followed by an appendix by A. Granier, that provides a quick introduction to the D-groupoid of a non-linear q-difference equation.