Timeline for What is the upper shriek in Grothendieck duality in the non-proper case?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 20, 2021 at 11:11 | vote | accept | Akhil Mathew | ||
| Apr 12, 2021 at 19:18 | answer | added | Peter Scholze | timeline score: 20 | |
| Aug 3, 2012 at 3:07 | comment | added | Moosbrugger | Doing it right is a non-trivial issue, discussed in some detail e.g. in arxiv.org/abs/1105.4857. But note that just defining it naively is easy: Nagata compactification exists for derived schemes as well. The analysis that this (homotopy) doesn't depend on the compactification essentially follows from the analysis in Section 6.2.2 of loc. cit. | |
| Aug 3, 2012 at 2:26 | comment | added | Akhil Mathew | Not really. I was just curious if there was any way of making the formalism clearer (e.g., a way of defining this functor which would generalize nicely to a derived setting). | |
| Aug 3, 2012 at 1:58 | comment | added | Moosbrugger | I'm afraid there's not really more to say than you've said. You have descriptions for open embeddings and proper morphisms and that's enough to describe it in general (say, for schemes finite type over a field). But $j^*=j^!$ doesn't commute with products (for $j$ an open embedding) and therefore doesn't have a left adjoint. Do you have a more precise question in mind? | |
| Aug 2, 2012 at 22:49 | answer | added | Jacob Bell | timeline score: 5 | |
| Aug 2, 2012 at 22:12 | history | asked | Akhil Mathew | CC BY-SA 3.0 |