Timeline for Representability of Grassmannian functor by a scheme
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2019 at 8:12 | comment | added | crystalline | Sadly I don’t really know a good textbook reference. The only thing I can suggest is maybe FGA explained, or also Toen’s Lecture notes ncatlab.org/nlab/show/Master+course+on+algebraic+stacks | |
| Jun 18, 2019 at 7:32 | comment | added | Luke | Thank you so much, this seems exactly like the kind of thing I wanted to see to get a feel for it. Do you happen to know any good references for it? I've been told SGA can be hard to follow. | |
| Jun 18, 2019 at 7:16 | comment | added | crystalline | Exactly! not sure if this spelled out in EGA unfortunately but it’s used frequently by people who work with the functor of points. | |
| Jun 18, 2019 at 6:48 | vote | accept | Luke | ||
| Jun 18, 2019 at 6:21 | comment | added | Luke | is this the kind of idea you are referring to? ncatlab.org/nlab/show/comparison+lemma | |
| Jun 18, 2019 at 6:06 | comment | added | Luke | Thank you for this answer, that does help a lot. I was wondering if I could clarify what you said about being sufficient to check this on affines. I know that once you show the functor is a Zariski sheaf, then you can assume WLOG that the base scheme $S$ is affine. But is reducing to the case where the scheme $T \rightarrow S$ is affine in EGA? Or is this what I have heard was developed by Deligne using projective limits of affines? | |
| Jun 17, 2019 at 19:47 | comment | added | crystalline | just to clarify, compactness wouldn't buy you anything anyway. Compactness is about maps out of your compact object, not into it. | |
| Jun 17, 2019 at 19:00 | history | answered | crystalline | CC BY-SA 4.0 |