Timeline for Schemes as a model category
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2010 at 15:50 | comment | added | Kevin H. Lin | Here's a nice nLab page on simplicial presheaves: ncatlab.org/nlab/show/model+structure+on+simplicial+presheaves | |
| Jun 30, 2010 at 0:53 | comment | added | Kevin H. Lin | algori: I didn't say that this can give a model structure wherein birational morphisms are weak equivalences. I agree with Andrea that this has probably little to do with birational geometry. I was thinking that this might be an answer to Andrea's first two questions, but probably not the third. | |
| Jun 29, 2010 at 23:19 | comment | added | Andrea Ferretti | I think this might be too big. I don't know how to make sense of the word birational in this context. I guess that the model category suggested by Kevin has little to do with birational geometry. | |
| Jun 29, 2010 at 18:12 | comment | added | Ben Wieland | Some people use "space" synonymously with "etale sheaf." Then the "algebraic" in "algebraic space" becomes a finiteness condition. | |
| Jun 29, 2010 at 17:51 | comment | added | algori | norondion -- could you elaborate on that please? Kevin -- to define sheaves (as opposed to presheaves) one needs a (Grothendieck) topology. What is the topology on $Sch_k$ that gives birational isomorphisms as weak equivalences after applying the construction in the paper you cite? | |
| Jun 29, 2010 at 17:36 | comment | added | Kevin H. Lin | To expand on this: You can embed Sch into the category of sheaves on Sch and then into the category of simplicial sheaves on Sch. One can then give the category of simplicial sheaves the structure of a closed simplicial model category. See for example section 2 of this: math.berkeley.edu/~teleman/math/simpson.pdf | |
| Jun 29, 2010 at 15:50 | history | answered | user19475 | CC BY-SA 2.5 |