Rangs et types de rang maximum dans les corps différentiellement clos

Abstract

AbstractIt is known that in differentially closed fields of characteristic zero, the ranks of stability RU, RM and the topological rank RH need not to be equal. Pillay and Pong have just shown however that the ranks RU and RM coincide in a group definable in this theory. At the opposite, we will show in this paper that the ranks RM and RH of a definable group can also be different, and even lead to non-equivalent notions of generic type.