Timeline for Specialization map étale cohomology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 18, 2018 at 6:40 | comment | added | Will Sawin | @AG2073951378 For lisse sheaves on non-henselian schemes the specialization map does go from $\eta$ to $s$. More precisely, there is a map from global sections to the stalk at $\eta$ and a map from global sections to the stalk at $s$. The first map is an isomorphism in the lisse case (as long as the scheme is normal, otherwise just an injection). The second map is an isomorphism in the Henselian case. | |
| Feb 18, 2018 at 2:27 | comment | added | user95222 | Can one relax the henselianity assumption on $R$ in any way? Probably not | |
| Feb 17, 2018 at 13:03 | vote | accept | CommunityBot | ||
| Feb 17, 2018 at 12:10 | comment | added | Will Sawin | For a general sheaf, the natural specialization map actually goes the other way. Given a section at $s$, you obtain a section over an etale neighborhood of $s$, which wlog is $R$ because $R$ is henselian, and hence a section at $\eta$. | |
| Feb 17, 2018 at 12:08 | history | answered | Will Sawin | CC BY-SA 3.0 |