Local models of Shimura varieties

One of the most famous results on the reduction of Shimura varieties (which goes back in its origins to Kronecker) describes the reduction modulo p of the modular curve with Γ(p)-level structure as the union of two copies of the modular curve crossing transversely at all supersingular points. In particular, this reduction is semi-stable, which decribes its local structure. The aim of  this project is to study the local structure of the reduction modulo p of general Shimura varieties by means of  the theory of local models of Shimura varieties.