Timeline for Is there a functor of points approach to algebraic cycles and intersection theory?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2020 at 0:14 | comment | added | R. van Dobben de Bruyn | One thing that comes to mind is bivariant intersection theory (see e.g. chapter 17 of Fulton), which is used for Riemann–Roch on singular varieties. But this assumes quite a bit about Chow groups already, so it's very far from a ground-up approach to functor of points intersection theory. | |
| Oct 6, 2016 at 2:55 | comment | added | Vladimir Baranovsky | Do you mean effective cycles, or arbitrary, up to rational equivalence or by themselves? There is an example of classes of zero cycles on a K3 surface, which - if I remember it right - cannot be represented by a scheme (or even a stack). | |
| Aug 27, 2016 at 6:48 | comment | added | tttbase | You might look at Triangulated categories of motives in positive characteristic by Shane Kelly where there is a definition of presheaves of relative cycles. | |
| Jun 23, 2014 at 8:21 | comment | added | jmc | @JoeB — Thanks for the references! As I wrote in the edit, by now I'm pretty satisfied with the usual approach. Nevertheless, it sounds interesting, and I will have a look at the papers you mentioned. | |
| Jun 22, 2014 at 19:32 | comment | added | Joe Berner | I'm not sure how much this satisfies you, but I did a little bit of a literature search and I found that several people have at least tried to do intersection theory on stacks. It's not exactly what you asked for but at least stacks are done F.O.P. style. In Gillet's "Intersection theory on algebraic stacks and $Q$-varieties" ('84), he says this goes back to Mumford looking at $\mathfrak{M}_g$ in "Towards an enumerative geometry of the moduli space of curves" ('83). I think after that was Gillet paper I mentioned, followed by Vistoli('89), Joshua('99), and more recent work by Gillet('09). | |
| Nov 22, 2013 at 10:04 | history | edited | jmc | CC BY-SA 3.0 |
Improves formatting, adds edit with new info/motivation/literature
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| Nov 6, 2012 at 3:11 | history | asked | jmc | CC BY-SA 3.0 |