Timeline for What are the easiest cases of base change (for sheaves on sites)?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2011 at 3:27 | comment | added | Mikhail Bondarko | Dear Alex, thanks! I fixed direct/inverse images, and will think about your words. | |
| Oct 11, 2011 at 3:18 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
fixed an error; added more detail
|
| Oct 10, 2011 at 21:24 | comment | added | Alex | I don't think that this can be true for general reasons. You write "It seems that I can prove it (using the fact that the inverse images are exact when we 'change topology on the same category'; hence the corresponding inverse images respect injective objects)", which doesn't make sense to me because there are too many inverse image functors in that sentence. Anyway, inverse image functors are always exact, so I'm going to assume you mean "direct images" the first time, and then I think that your sentence is not true (it seems that it would imply that the global sections functor is exact). | |
| Oct 10, 2011 at 20:30 | comment | added | algori | Mikhail -- I've fixed the Latex. It seems that Mathjacks goes gaga once it sees an asterisk. | |
| Oct 10, 2011 at 20:28 | history | edited | algori | CC BY-SA 3.0 |
Latex fix
|
| Oct 10, 2011 at 20:01 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
added some details
|
| Oct 10, 2011 at 19:03 | comment | added | Alex | Sorry, but there are too many ways to interpret your question. Can you write exactly which morphisms of sites you are considering, and which direct image functors should commute with which inverse image functors ? By the way, you "trivial topology" is classically called "chaotic" or "coarse" (cf SGA 4 II 1.1.4). | |
| Oct 10, 2011 at 13:46 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
added 127 characters in body
|
| Oct 10, 2011 at 13:38 | history | asked | Mikhail Bondarko | CC BY-SA 3.0 |