# A p-adic analogue of an algebraization theorem of Borel

## Location

383N

Monday, January 23, 2023 2:30 PM

Abhishek Oswal (Caltech)

Let S be a Shimura variety such that the connected components of the set of complex points S(C) are quotients of Hermitian symmetric domains by torsion-free arithmetic groups. Borel then proved that any holomorphic map from a complex algebraic variety into the complex-analytic space S(C) is an algebraic map. In this talk I shall describe ongoing work with Ananth Shankar and Xinwen Zhu, where we prove a p-adic analogue of this result of Borel for certain Shimura varieties of abelian type.