Timeline for Are all Shimura Varieties Special Subvarieties of the Siegel modular Variety?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2011 at 15:54 | comment | added | Keerthi Madapusi | Ah, yes, they must be of pure $D$-type. Thank you for the correction. | |
| Mar 9, 2011 at 11:37 | comment | added | Mikhail Borovoi | It is not quite correct that the answer does not depend on the $\mathbb{Q}$-structure. For example, let $G$ be a $\mathbb{Q}$-group such that the decomposition of $G_{\mathbb{R}}$ into a product of simple $\mathbb{R}$-groups contains both $\mathrm{SO}(8,2)$ and $\mathrm{SO}^*(10)$ (and only these $\mathbb{R}$-groups). If $G$ is a product of $\mathbb{Q}$-abolutely-simple groups, then a Shimura datum $(G,X)$ admits a symplectic embedding. However, if $G$ is $\mathbb{Q}$-simple, then $(G,X)$ has no symplectic embeddings. | |
| Mar 9, 2011 at 5:28 | comment | added | Keerthi Madapusi | Yes, the question doesn't depend on the $\mathbb{Q}$-structure; see 2.3.10 in Deligne's article. You have to be careful to distinguish between a Shimura variety and its (geometrically) connected components. In general, only the latter can be quotients of the upper half plane. | |
| Mar 8, 2011 at 22:41 | comment | added | jacob | Thanks! Just so I understand, for the classical groups, the answer is yes independantly of the $\mathbb{Q}$-structure? So for instance, for any Shimura variety arising as a quotient of the Siegel upper half plane? | |
| Mar 8, 2011 at 22:39 | vote | accept | jacob | ||
| Mar 8, 2011 at 21:17 | history | answered | Keerthi Madapusi | CC BY-SA 2.5 |