Timeline for Does there exist a scheme $X/{\operatorname{Spec}(\mathbb{Z})}$ such that $\pi_1^\text{ét}(X)=\smash{\hat{\mathbb{Z}}}^2$?
Current License: CC BY-SA 4.0
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| Sep 11 at 18:58 | comment | added | Will Chen | (this is kind of like the approach to moduli problems. Even if the moduli-thing isn't a scheme, you shouldn't stop there. Instead, first note that the moduli-thing is tautologically a category. Then you show maybe that it's a stack, maybe even a Deligne-Mumford stack, maybe even smooth, maybe even an algebraic space, maybe even a scheme! At each stage you can also identify the obstructions to the desired thing lying in the smaller category. This way you can get a much better understanding of the situation.) | |
| Sep 11 at 18:54 | comment | added | Will Chen | @RJAcuña It's a legit question. It's just that there aren't that many subschemes of Spec $\mathbb{Z}$, so the answer is not that interesting. You might be able to ask a better question by enlarging the category of possible answers so that the answer is tautologically "yes", and then asking for the smallest/nicest subcategory that contains your desired object. My answer shows that the desired object is not a subscheme, but maybe if you relax the requirements a bit it is a sub(something). | |
| Sep 11 at 14:57 | comment | added | RJ Acuña | Given that you mentioned “as stated” what would be the legit question that could have interesting answers? | |
| Sep 11 at 14:54 | vote | accept | RJ Acuña | ||
| Sep 11 at 5:19 | history | answered | Will Chen | CC BY-SA 4.0 |