Timeline for Schemes as a model category
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2010 at 23:20 | comment | added | Andrea Ferretti | @Tom: a map which is an isomorphism on dense open subschemes. Me too, I'd rather work with varieties, but then you don't have even colimits. | |
| Jun 29, 2010 at 22:04 | comment | added | D.-C. Cisinski | We might invert dense open immersions between k-schemes of finite type. A convenient way to study this localization consists to look at the model category of simplicial presheaves on $Sch/k$, and then to look at its left Bousfield localization by dense open immersions. What we get is very interesting, and leads to beautiful results and problems, related to $\pi_0$ in $A^1$-homotopy theory of schemes). This is studied by Fabien Morel and Aravind Asok in their papers arXiv:0810.0324 and arXiv:1001.4574 (even though they don't formulate things this way explicitly). | |
| Jun 29, 2010 at 21:45 | comment | added | Tom Goodwillie | What is meant by a birational map between arbitrary schemes of finite type over a field? | |
| Jun 29, 2010 at 18:28 | comment | added | Charles Rezk | I have the vague sense that someone has thought about what happens if you formally invert the class of birational maps in the category schemes, and decided that what you get isn't very interesting. I actually thought that had been asked here before, but I can't find it. | |
| Jun 29, 2010 at 17:30 | comment | added | Mariano Suárez-Álvarez | For 1, googling for "finite limit completion" shows such a thing exists, but I am not lucky enough to get details... | |
| Jun 29, 2010 at 15:50 | answer | added | user19475 | timeline score: 6 | |
| Jun 29, 2010 at 15:36 | history | asked | Andrea Ferretti | CC BY-SA 2.5 |