Timeline for Fpqc-locally constant if and only if étale-locally constant?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2021 at 13:54 | vote | accept | Z Wu | ||
| Mar 17, 2021 at 21:17 | comment | added | Peter Scholze | You have to see that the sheaf $S\mapsto \mathrm{Aut}(M|_S)$ is representable by a scheme that is a disjoint union of copies of $S$ (for the claim that $\mathcal G$ is locally constant, and an $\mathrm{Aut}(M)$-torsor). In the language of condensed mathematics, this amounts to showing that $\mathrm{Aut}(M)$ is discrete, but there are other direct ways of arguing. | |
| Mar 17, 2021 at 20:32 | comment | added | Wille Liu | @PeterScholze Can you explain a bit how that discrete topology on $\mathrm{Aut}(M)$ intervenes? | |
| Mar 17, 2021 at 19:41 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Mar 17, 2021 at 19:41 | comment | added | Peter Scholze | Of course, Thanks! Edited | |
| Mar 17, 2021 at 17:01 | comment | added | Matt E | In the final para., do you mean the nodal $\mathbb P^1$? | |
| Mar 17, 2021 at 12:19 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Mar 17, 2021 at 11:04 | history | edited | Peter Scholze | CC BY-SA 4.0 |
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| Mar 17, 2021 at 10:04 | history | answered | Peter Scholze | CC BY-SA 4.0 |