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Congruence relations on some Shimura varieties. (English) Zbl 1101.14033
Summary: The main purpose of this paper is the generalization of the well-known Eichler-Shimura congruence relations for modular curves to Shimura varieties of PEL type whose Shimura group \(G\) is split over a fixed prime \(p\). In particular we prove a conjecture of Blasius and Rogawski for these Shimura varieties. Further we give a formula for the cycle which is the reduction to positive characteristic of the Hecke operator \(T_p\) in terms of the root data of \(G\) and calculate this cycle in two examples.

MSC:
14G35 Modular and Shimura varieties
11G18 Arithmetic aspects of modular and Shimura varieties
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