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Romolo
Romolo
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For a connected reductive group $G/\mathbb{Q}$ what is known about the minimum level such that the respective principal congruence subgroup is the intersection of a neat open compact subgroup of $G(\mathbb{A}_f)$ and $G(\mathbb{Q})$?

For $GL_2$ the answer is $3$.

For a connected reductive group $G/\mathbb{Q}$ what is known about the minimum level such that the respective principal congruence subgroup is the intersection of a neat open compact subgroup of $G(\mathbb{A}_f)$ and $G(\mathbb{Q})$?

For a connected reductive group $G/\mathbb{Q}$ what is known about the minimum level such that the respective principal congruence subgroup is the intersection of a neat open compact subgroup of $G(\mathbb{A}_f)$ and $G(\mathbb{Q})$?

For $GL_2$ the answer is $3$.

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Romolo
Romolo
  • 11
  • 2

Minimum level principal congruence subgroup coming from neat open compact subgroup

For a connected reductive group $G/\mathbb{Q}$ what is known about the minimum level such that the respective principal congruence subgroup is the intersection of a neat open compact subgroup of $G(\mathbb{A}_f)$ and $G(\mathbb{Q})$?