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Hi,

I haveSuppose that one has a vague question but am looking forShimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a non-vague answermoduli space of motives (i.e., concrete statements, results, references, etc..g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). My questionWhat is: the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

  • Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). What is the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

(References for the exact definition of motivic Galois group being used in the answer would also be appreciated).

Thanks!

Hi,

I have a vague question but am looking for a non-vague answer (i.e., concrete statements, results, references, etc...). My question is:

  • Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). What is the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

(References for the exact definition of motivic Galois group being used in the answer would also be appreciated).

Thanks!

Hi,

Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). What is the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

(References for the exact definition of motivic Galois group being used in the answer would also be appreciated).

Thanks!

Source Link
unknown
unknown
  • 647
  • 4
  • 8

Motivic Galois group and Shimura varieties

Hi,

I have a vague question but am looking for a non-vague answer (i.e., concrete statements, results, references, etc...). My question is:

  • Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). What is the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

(References for the exact definition of motivic Galois group being used in the answer would also be appreciated).

Thanks!