Timeline for algebraization theorems
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2014 at 15:59 | answer | added | Jonathan Wise | timeline score: 6 | |
| Feb 21, 2013 at 8:26 | comment | added | ACL | Jean-Benoît Bost reminded my that in SGA 2, Exposé IX, Grothendieck proves a comparison theorem between formal and algebraic cohomology which works beyond the proper case. In the following Exposés, he gives applications to fundamental groups and Picard groups. | |
| Feb 6, 2013 at 17:40 | answer | added | ACL | timeline score: 12 | |
| Feb 6, 2013 at 8:57 | answer | added | David Rydh | timeline score: 6 | |
| Jan 1, 2013 at 6:38 | comment | added | anon | Faltings proved a few algebraisation results in the late 70s and early 80s in the setting of local algebra that were considerably deeper than any previously known results; see MR0554381 for a lovely example involving algebraisation of formal cohomology groups. (He used these to prove new algebraisation (and topological) results in projective geometry.) | |
| Jan 3, 2012 at 15:30 | comment | added | Jason Starr | @Roessler: There is an algebraization theorem due to Toen for analytic stacks. However, my impression is that this uses Grothendieck's existence theorem. | |
| Jan 3, 2012 at 7:51 | comment | added | Damian Rössler | That is also my impression. I guess that to get a feeling fo this, one should first look for algebraization results in the analytic world (ie over $\bf C$). Are there any general algebraization results for certain classes of open complex analytic manifolds ? (I don't know of any). | |
| Jan 3, 2012 at 4:32 | comment | added | Jason Starr | This isn't an answer, just an opinion. I have never heard of any other algebraization theorems; I think they all reduce to the ones you already know. | |
| Jan 1, 2012 at 7:02 | history | asked | Jonathan Wise | CC BY-SA 3.0 |