Rangs et types de rang maximum dans les corps différentiellement clos

Abstract

It 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.