Abhishek Oswal

Caltech

## Time:

Thursday, November 17, 2022 - 3:00pm to 4:00pm

## Location:

RH 306
Let S be a Shimura variety such that the connected components of the set of complex points $S(\mathbb{C})$ are of the form $D/\Gamma$, where $\Gamma$ is a torsion-free arithmetic group acting on the Hermitian symmetric domain $D$. Borel proved that any holomorphic map from any complex algebraic variety into $S(\mathbb{C})$ is an algebraic map. In this talk I shall describe ongoing joint work with Ananth Shankar and Xinwen Zhu, where we prove a $p$-adic analogue of this result of Borel for compact Shimura varieties of abelian type.