Résume | The aim of the talk is to develop a Picard-Vessiot theory fordifferential equations in positive characteristic which is quiteanalogue to the characteristic zero theory. This is achieved bysubstituting ordinary differential equations by differential modulesand equations for higher (iterative) derivations. With thismodification it is possible to solve the inverse Galois problem inpositive characteristic at least for connected linear groups and toprove an analogue of the Abhyankar conjecture. This finally explainssome of the Ramis-Raynaud analogies. The lecture is based on commonwork with M. van der Put.B.H. Matzat, M. v.d.Put: Iterative differential equations and theAbhyankar conjecture. Preprint 2001. |