Sebastian Eterović: Categoricity of Shimura Varieties

Abstract: I will show how a conjecture of Pink on Galois representations attached to points in Shimura varieties can be equivalently stated in model-theoretic terms as the question of categoricity. Most of the arguments can be expressed in geometric terms, and I will explain the model-theoretic background that is needed. This equivalence shows that the openness of Galois representations is intimately related to the structure of special subvarieties in the Shimura variety.