Timeline for Map from the stack of coherent sheaves on a curve to the Grothendieck group
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2020 at 12:45 | comment | added | Jason Starr | I do not know about the general case, and I doubt that the K-group has a natural structure of algebraic stack (think about the associated graded that is the Chow group). For curves, this is “classical”. One construction using the determinant of a perfect complex is given in Definition 2.11 of my article with de Jong and He. | |
| Dec 4, 2020 at 12:09 | comment | added | hennlu | Thanks ! Is it something obvious that can be generalized to any category having a moduli stack of objects ? I assume we also have to define a algebraic stack structure for the Grothendieck group. Do you have any reference where I can have a look to get a better understanding of this ? | |
| Dec 4, 2020 at 11:36 | comment | added | Jason Starr | Yes, there is a 1-morphism of algebraic stacks as you describe. | |
| Dec 4, 2020 at 11:29 | history | asked | hennlu | CC BY-SA 4.0 |