Timeline for An extension of the Galois theory of Grothendieck
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2021 at 11:19 | vote | accept | user1005113 | ||
| Dec 27, 2021 at 11:09 | history | edited | user1005113 | CC BY-SA 4.0 |
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| Dec 26, 2021 at 2:14 | history | became hot network question | |||
| Dec 25, 2021 at 23:36 | history | edited | LSpice | CC BY-SA 4.0 |
Links and name of paper
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| Dec 25, 2021 at 23:20 | history | edited | YCor | CC BY-SA 4.0 |
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| Dec 25, 2021 at 20:02 | answer | added | Simon Henry | timeline score: 19 | |
| Dec 25, 2021 at 19:55 | comment | added | Maxime Ramzi | @BenjaminSteinberg you're right, I don't know what I was thinking : the result in question exactly proves this :D it is indeed possible a priori | |
| Dec 25, 2021 at 19:49 | comment | added | Benjamin Steinberg | @MaximeRamzi I believe that morota equivalence is the same as natural equivalence for profinite groupoids. I'm less certain there isn't a non profinite localic groupoid with the same topos | |
| Dec 25, 2021 at 19:49 | answer | added | Maxime Ramzi | timeline score: 8 | |
| Dec 25, 2021 at 19:33 | comment | added | Maxime Ramzi | @BenjaminSteinberg : in the case of a profinite group(oid), I think you can recover it completely up to equivalence - I don't know if it was known before in this generality, but at the very least it's worked out in Akhil Mathew's "The Galois group of a stable homotopy theory" as theorem 5.36 (which gets rid of the fiber functor needed for Grothendieck's theorem) | |
| Dec 25, 2021 at 19:21 | comment | added | Benjamin Steinberg | The continuous G-sets for a profinite group is an example of equivariant sheaves on a localic groupoid. That being said the groupoid in general is only unique up to an appropriate notion of Morita equivalence. But I'm not an expert so I can't say for sure if their proof recovers the fundamental group but it probably does. | |
| Dec 25, 2021 at 18:13 | history | asked | user1005113 | CC BY-SA 4.0 |