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jacob
jacob
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Question: Let $S$ be a 0-dimensional Shimura variety. Does $S$ necessarily admit a morphism (in the category of Shimura varieties) to $\mathcal{A}_g$ for some $g\geq 1$? Here $\mathcal{A}_g$ is the moduli space of principally polarized abelian varieties.

Motivation: Basically, I am trying to understand something for all Shimura varieties. This reduces to some statement adnabout 0-dimensional Shimura varieties, and iI wanna see if I can apply techniques from the theory of Abelian Varieties to do so.

Question: Let $S$ be a 0-dimensional Shimura variety. Does $S$ necessarily admit a morphism (in the category of Shimura varieties) to $\mathcal{A}_g$ for some $g\geq 1$? Here $\mathcal{A}_g$ is the moduli space of principally polarized abelian varieties.

Motivation: Basically, I am trying to understand something for all Shimura varieties. This reduces to some statement adn 0-dimensional Shimura varieties, and i wanna see if I can apply techniques from the theory of Abelian Varieties to do so.

Question: Let $S$ be a 0-dimensional Shimura variety. Does $S$ necessarily admit a morphism (in the category of Shimura varieties) to $\mathcal{A}_g$ for some $g\geq 1$? Here $\mathcal{A}_g$ is the moduli space of principally polarized abelian varieties.

Motivation: Basically, I am trying to understand something for all Shimura varieties. This reduces to some statement about 0-dimensional Shimura varieties, and I wanna see if I can apply techniques from the theory of Abelian Varieties to do so.

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jacob
jacob
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  • 18
  • 22

Do all 0-dimensional Shimura Varieties show up (as CM points) in $\mathcal{A}_g$?

Question: Let $S$ be a 0-dimensional Shimura variety. Does $S$ necessarily admit a morphism (in the category of Shimura varieties) to $\mathcal{A}_g$ for some $g\geq 1$? Here $\mathcal{A}_g$ is the moduli space of principally polarized abelian varieties.

Motivation: Basically, I am trying to understand something for all Shimura varieties. This reduces to some statement adn 0-dimensional Shimura varieties, and i wanna see if I can apply techniques from the theory of Abelian Varieties to do so.