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ali
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Deligne's idea was that Shimura varieties should be understood as moduli space of motives(with extra structures). lot's of Shimura varieties of abelian type can be understood as moduli space of abelian motives and any way essentially you can study all of them in this way by using Deligne formalism about the relation between two isogenous Shimura datum.

but there are Shimura varieties that are not of abelian type. My question is if there is any such Shimura variety that has a "nice" moduli description. I prefer examples that you can do explicit computations with them if such examples exist.

(In general, I appreciate any good reference about Shimura varieties of not abelian type)?

Deligne's idea was that Shimura varieties should be understood as moduli space of motives(with extra structures). lot's of Shimura varieties of abelian type can be understood as moduli space of abelian motives and any way essentially you can study all of them in this way by using Deligne formalism about the relation between two isogenous Shimura datum.

but there are Shimura varieties that are not of abelian type. My question is if there is any such Shimura variety that has a "nice" moduli description. I prefer examples that you can do explicit computations with them if such examples exist.

(In general, I appreciate any good reference about Shimura varieties of not abelian type)

Deligne's idea was that Shimura varieties should be understood as moduli space of motives(with extra structures). lot's of Shimura varieties of abelian type can be understood as moduli space of abelian motives and any way essentially you can study all of them in this way by using Deligne formalism about the relation between two isogenous Shimura datum.

but there are Shimura varieties that are not of abelian type. My question is if there is any such Shimura variety that has a "nice" moduli description?

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ali
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Shimura varieties which are not of abelian type but has a good modular description

Deligne's idea was that Shimura varieties should be understood as moduli space of motives(with extra structures). lot's of Shimura varieties of abelian type can be understood as moduli space of abelian motives and any way essentially you can study all of them in this way by using Deligne formalism about the relation between two isogenous Shimura datum.

but there are Shimura varieties that are not of abelian type. My question is if there is any such Shimura variety that has a "nice" moduli description. I prefer examples that you can do explicit computations with them if such examples exist.

(In general, I appreciate any good reference about Shimura varieties of not abelian type)