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Automorphism groups of Shimura varieties. (English) Zbl 1178.11049

Summary: 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 G. Shimura [Ann. Math. (2) 91, 144–222 (1970; Zbl 0237.14009)], P. Deligne [Automorphic forms, representations and L-functions, Proc. Symp. Pure Math. Am. Math. Soc., Corvallis/Oregon 1977, Proc. Symp. Pure Math. 33, No. 2, 247–290 (1979; Zbl 0437.14012)] and J. S. Milne and K. Shih [Am. J. Math. 103, 911–935 (1981; Zbl 0475.14022)].

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
11G25 Varieties over finite and local fields
11G15 Complex multiplication and moduli of abelian varieties
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