Abstract: Local models of Shimura varieties are projective flat schemes over the spectrum of a discrete valuation ring. The importance of the local models lies in the fact that under some assumptions they model the singularities that arise in the reduction modulo p of Shimura varieties. In this talk, we will give an explicit description of some orthogonal and unitary local models. Then, we will build on this and we will resolve the singularities of these models. This will lead to regular integral models for the corresponding Shimura varieties.
