Timeline for DAG vs Classical algebraic geometry
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2019 at 3:08 | comment | added | Maanroof | Right. I guess right now I'm more looking for similarities than differences. For example, from the perspective of derived schemes, these derived fiber products still behave like intersection, right? E.g., I believe that the non-empty fibers of open immersions are given by fields. Basically, my question is: does one need to prove all of the expected behavior one statement at a time, or is there some general machinery for this? | |
| Mar 31, 2019 at 2:52 | comment | added | JJJ | One of the traditional motivations is intersection theory. If you consider two ordinary affine schemes $SpecR$, $SpecS$ over a base $SpecA$, then their fibered product as schemes is given by $Spec(R\otimes_A S)$. However if we consider them as constant derived schemes, then their fibered product as such is the affine derived scheme $Spec(R \otimes^L _A S)$ (derived tensor product of simplicial rings). The significance of this is that the derived fibered product remembers all the $Tor^A_n(R,S)$. So by Serre's intersection formula, derived intersections remember all intersection multiplicities. | |
| Mar 31, 2019 at 2:30 | history | asked | Maanroof | CC BY-SA 4.0 |