Timeline for Geometric points in geometry agree with "geometric points" of the Zariski topos
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2018 at 7:48 | comment | added | Harry Gindi | @W. Rether I think this is in Hakim's, Giraud's, or Illusie's thesis. I completely forgot which one, since it has been a while. | |
| Jul 1, 2018 at 17:29 | comment | added | W.Rether | Can you tell me how (or where) does Grothendieck prove that last correspondence? I know how to obtain a point of the topos (a functor from the étale topos to Sets that commutes with colimits and finite limits) given a geometric point of the scheme $Spec(k(s)_{sep})→S$. But how do I prove "the converse" (i.e. that this is an equivalence)? | |
| S Jun 16, 2017 at 7:35 | history | suggested | Topological | CC BY-SA 3.0 |
Added topos tag
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| Jun 16, 2017 at 6:53 | review | Suggested edits | |||
| S Jun 16, 2017 at 7:35 | |||||
| Dec 10, 2010 at 10:04 | comment | added | BCnrd | The geom. pts of topos of a sober top. space (e.g., scheme, loc. Hausdorff space), are (up to equiv.) stalk functors at pts of the top. space, with distinct physical pts giving inequiv. functors. (For a scheme $S$ can use pullback along Spec($\overline{k(s)}) \rightarrow S$, but silly since Spec($\overline{k(s)}) \rightarrow {\rm{Spec}}(k(s))$ induces equiv. of Zariski topoi.) This is proved in "Sheaves in Geom. & Logic" and near end of 2nd volume of SGA4, where Grothendieck proves that geom. pts of etale topos of $S$ are (up to equiv.) pullbacks along Spec($k(s)_{\rm{sep}}) \rightarrow S$. | |
| Dec 10, 2010 at 6:44 | comment | added | Harry Gindi | Obviously by Zariski and étale toposes, I mean the appropriate slicey-guys over a scheme. | |
| Dec 10, 2010 at 6:18 | history | asked | Harry Gindi | CC BY-SA 2.5 |