Timeline for Rigidity of the category of schemes
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2017 at 4:42 | comment | added | R. van Dobben de Bruyn | Maybe you can use this to determine all fields by viewing which finitely generated fields sit inside it. The idea is to use Pop's extension of the Neukirch–Uchida theorem to all finitely generated infinite fields of arbitrary characteristic (up to purely inseparable morphisms, which are not detected by the Galois group), cf. Pop's article in the 1997 Obergurgl proceedings on Resolution of Singularities. I haven't worked this out carefully, and I anticipate some problems (e.g. purely separable extensions). | |
| Dec 18, 2017 at 4:16 | comment | added | R. van Dobben de Bruyn | I think you can also use the Neukirch–Uchida theorem, which states that number fields with isomorphic Galois groups are isomorphic. I think we can recover the Galois group with its profinite group structure from the category of schemes as well. | |
| Mar 16, 2011 at 23:35 | comment | added | Martin Brandenburg | I can't prove your universal property of $\text{Spec } \mathbb{Z}_{(p)}$, but the following works: It is the unique connected scheme together with a bijektive morphism from $\text{Spec } \mathbb{F}_p \coprod \text{Spec } \mathbb{Q}$. | |
| Mar 1, 2011 at 9:21 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |