GALOIS GROUPS OF DIFFERENCE EQUATIONS OF ORDER TWO ON ELLIPTIC CURVES

Thomas Dreyfus (1) , Julien Roques (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IF - Institut Fourier

This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups. For instance, our results combined with a result from transcendence theory due to Schneider allow us to identify a large class of discrete Lamé equations with difference Galois group GL2(C).

Domaines: Mathématiques générales [math.GM]

Thomas Dreyfus, Julien Roques. GALOIS GROUPS OF DIFFERENCE EQUATIONS OF ORDER TWO ON ELLIPTIC CURVES. Symmetry, Integrability and Geometry : Methods and Applications, 2015, ⟨10.3842/SIGMA.2015.003⟩. ⟨hal-01897304⟩