Hida, Haruzo Automorphism groups of Shimura varieties. (English) Zbl 1178.11049 Doc. Math. 11, 25-56 (2006). 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)]. Cited in 2 Documents 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 Keywords:Shimura variety; reciprocity law Citations:Zbl 0237.14009; Zbl 0437.14012; Zbl 0475.14022 PDFBibTeX XMLCite \textit{H. Hida}, Doc. Math. 11, 25--56 (2006; Zbl 1178.11049) Full Text: EuDML EMIS