Abstract
In the first three sections we review the definition of a Shimura variety of abelian type, describe how certain Shimura varieties are moduli varieties for abelian varieties with Hodge cycles and level structure, and prove a result concerning reductive groups that will frequently enable us to replace one such group by a second whose derived group is simply connected.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-540-38955-2_16
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References
Deligne, P. Travaux de Shimura, Sém. Bourbaki Février 71, Exposé 389, Lecture Notes in Math., 244, Springer, Berlin, 1971.
Deligne, P. Variétés de Shimura: interpretation modulaire, et techniques d construction de modéles canoniques. Proc. Symp. Pure Math., A.M.S. 33 (1979) part 2, 247–290.
Deligne, P. Valeurs de fonctions L et périodes d’intégrales. Proc. Symp. Pure Math., A.M.S., 33 (1979) part 2, 313–346.
Doi, K. and Naganuma, H. On the algebraic curves uniformized by arithmetical automorphic functions. Ann. Math. 86 (1967) 449–460.
Kazhdan, D. On arithmetic varieties. Lie Groups and their representations, Halsted, New York, 1975. 158–217.
Langlands, R. Some contemporary problems with origins in the Jugendtraum. Proc. Symp. Pure Math., A.M.S. 28(1976) 401–418.
Langlands, R. Conjugation of Shimura varieties (preliminary version of [3]).
Langlands, R. Automorphic representations, Shimura varieties, and motives. Ein Märchen. Proc. Symp. Pure Math., A.M.S., 33 (1979) part 2, 205–246.
Milne, J. and Shih, K.-y. The action of complex conjugation on a Shimura variety, Annals of Math, 113 (1981) 569–599.
Serre, J.-P. Cohomologie Galoisienne, Lecture Notes in Math. 5, Springer, Berlin, 1964.
Shih, K.-y. Anti-holomorphic automorphisms of arithmetic automorphic function fields, Ann. of Math. 103 (1976) 81–102.
Shih, K.-y. Conjugations of arithmetic automorphic function fields, Invent. Math. 44 (1978) 87–102.
Shimura, G. Introduction to the arithmetic theory of automorphic functions. Princeton Univ. Press 1971.
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Milne, J.S., Shih, K.y. (1982). Conjugates of Shimura Varieties. In: Hodge Cycles, Motives, and Shimura Varieties. Lecture Notes in Mathematics, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38955-2_7
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DOI: https://doi.org/10.1007/978-3-540-38955-2_7
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