Automorphism groups of Shimura varieties

Abstract

In this paper, we determine the scheme automorphism group of the reduction modulo $p$ of the integral model of the connected Shimura variety (of prime-to-$p$ level) for reductive groups of type $A$ and $C$. The result is very close to the characteristic 0 version studied by Shimura, Deligne and Milne-Shih.