Timeline for To what extent are modular parametrizations expected to generalize?
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| Feb 22, 2017 at 9:20 | history | edited | Olivier | CC BY-SA 3.0 |
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| Sep 9, 2015 at 0:01 | comment | added | Miles Lake | For example, the Blasius paper says that the elliptic curve corresponding to (certain) Hilbert automorphic representations are not quotients of Albanese of any Shimura variety (even in the real quadratic case), but he does realize the curve in an abelian variety he constructs by hand, so I suppose my follow-up would be along the lines of “can one always systematically construct something like this variety?”, "Does such a conjecture follow from any of the big standard conjectures?", or “Is the abelian variety he constructs a Jacobian of some curve that admits a map to the elliptic curve?” | |
| Sep 8, 2015 at 23:58 | comment | added | Miles Lake | Thanks for your answer! I suppose this generalization is not so surprising, since most varieties wouldn’t be nice quotients of abelian varieties, and even more so from a restricted class like Picards of Shimura varieties. However, I was wondering if there was anything beyond the case of Shimura varieties, which is one reason why I didn’t restrict the question to them. Referring again to the function field analogue (e.g. D-elliptic sheaves, positive-char uniformizations), one does not have to parametrize a variety (say, abelian) by some moduli space of the same kind of variety. | |
| Sep 8, 2015 at 13:42 | history | edited | Olivier | CC BY-SA 3.0 |
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| Sep 7, 2015 at 9:36 | history | answered | Olivier | CC BY-SA 3.0 |