Timeline for Useful invariants of etale topoi not coming from the shape
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2019 at 17:29 | comment | added | Todd Trimble | meta.mathoverflow.net/questions/4200/flood-of-similar-new-users | |
| Jun 3, 2019 at 16:46 | answer | added | Denis Nardin | timeline score: 10 | |
| Jun 3, 2019 at 16:43 | comment | added | Harry Gindi | @DenisNardin Be my guest. =] | |
| Jun 3, 2019 at 15:52 | comment | added | Denis Nardin | @HarryGindi Are you going to write it as an answer? Otherwise I am going to do so (btw the Galois category is a complete invariant of the étale topos for qcqs schemes) | |
| Jun 3, 2019 at 14:39 | comment | added | Harry Gindi | @cardinal I think this works, but I haven't done a lot of computations with this stuff yet: Consider the map from the complex affine line to spec C. The shape of both étale topoi is contractible, but the Galois category of A^1 is not equivalent to to the Galois category of Spec C. | |
| Jun 3, 2019 at 13:57 | comment | added | user74900 | @HarryGindi well, maybe consider cooking it up then (I am not saying it is your obligation, your comment is a comment, not an answer), but if you add that information that would make an answer. | |
| Jun 3, 2019 at 13:57 | comment | added | Harry Gindi | @cardinal It isn't. There is an equivalence of higher categories proven. All you need to do is cook up two distinct stratified spaces with the same realization with respect to the trivial stratification. | |
| Jun 3, 2019 at 13:40 | comment | added | user74900 | @HarryGindi I guess one also has to show that it is not determined by the shape of the topos :) | |
| Jun 3, 2019 at 12:55 | comment | added | Harry Gindi | Barwick, Glasman, and Haine have constructed a finer invariant that specializes to the shape under a realization called the Galois category, which is naturally stratified over the underlying space of a qcqs scheme. It is a delocalization of the étale homotopy type and determines the higher category of all non-abelian constructible sheaves. They also show that this stratified space determines the étale topos up to equivalence. maths.ed.ac.uk/~cbarwick/papers/exodromy.pdf | |
| Jun 3, 2019 at 11:35 | history | asked | user141417 | CC BY-SA 4.0 |