Parallélogrammes Galoisiens

We generalize the notion of a Galois extension by that of a Galois parallelogram; a Galois extension is just a flat Galois parallelogram. The existence of Galois parallelograms is proved in the number field case. We state numerous general properties of Galois parallelograms which give, in particular, the usual properties of classical Galois theory. Then, we introduce a “two-dimensional Galois theory” by generalizing to Galois parallelograms the classical Galois bijection for finite Galois extensions.