Timeline for If $R$ is an etale extension of $\mathbb Z$, then $R = \mathbb Z^n$?
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8 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2018 at 14:12 | comment | added | R. van Dobben de Bruyn | @მამუკაჯიბლაძე: admittedly, there might not be a reference that I truly like. Hartshorne leaves it at four exercises, and in EGA and the Stacks project it relies on a lot of theory already. A place to start could be Milne's notes on étale cohomology, or his book on the same subject (which is more technical). | |
| Jul 24, 2018 at 13:53 | comment | added | მამუკა ჯიბლაძე | @R.vanDobbendeBruyn Thanks! What would be your favorite text for that? | |
| Jul 24, 2018 at 13:47 | comment | added | R. van Dobben de Bruyn | @მამუკაჯიბლაძე: I don't know a reference that treats the affine case exclusively; only the more general setting of étale morphisms of schemes. Examples include $\operatorname{Spec} \mathbb Z[1/n]$ and finite étale extensions thereof (e.g. $\mathbb Z[\zeta_n][1/n]$, the integral closure of $\mathbb Z[1/n]$ in the ray class field of modulus $n \cup \infty$), as well as products of such. | |
| Jul 24, 2018 at 4:57 | comment | added | მამუკა ჯიბლაძე | @R.vanDobbendeBruyn Do you know where to read about non-finite étale $\mathbb Z$-algebras? | |
| Jul 23, 2018 at 19:59 | comment | added | R. van Dobben de Bruyn | A better term would be finite étale $A$-algebra, because there are also étale $A$-algebras that are not finite. | |
| Jul 23, 2018 at 19:50 | answer | added | skd | timeline score: 4 | |
| Jul 23, 2018 at 18:38 | comment | added | Keerthi Madapusi | This fact is equivalent to Minkowski's theorem. I do not know of a different proof. | |
| Jul 23, 2018 at 17:33 | history | asked | D_S | CC BY-SA 4.0 |