Algebra and Geometry Seminar

Let S be a Shimura variety such that the connected components of the set of complex points of S are quotients of Hermitian symmetric domains by torsion-free arithmetic subgroups. Borel then proved that any holomorphic map from a complex algebraic variety into S is in fact algebraic. In this talk, I'll talk about a p-adic analogue of this algebraization result. This is joint work with Anand Patel, Ananth Shankar and Xinwen Zhu.