The reduction of connected Shimura varieties at primes of good reduction

This thesis gives a modified version of the Langlands and Rapoport conjecture which allows us for the first time to state a conjecture about the reduction of connected Shimura varieties. The main result of this thesis says that under certain conditions the modified Langlands Rapoport conjecture is equivalent to the conjecture for connected Shimura varieties.;As an application we show that if the modified Langlands Rapoport conjecture is valid for Shimura varieties of PEL-type then it is true for Deligne's strange models. We establish the validity of the modified conjecture in the case of Siegel modular varieties.