Final Version; Final Form. Shimura Varieties and Motives
نویسندگان
چکیده
Deligne has expressed the hope that a Shimura variety whose weight is defined over Q is the moduli variety for a family of motives. Here we prove that this is the case for “most” Shimura varieties. As a consequence, for these Shimura varieties, we obtain an explicit interpretation of the canonical model and a modular description of its points in any field containing the reflex field. Moreover, when we assume the existence of a sufficiently good theory of motives in mixed characteristic, we are able to obtain a description of the points on the Shimura variety modulo a prime of good reduction.
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