Timeline for Can a Chow motif be isomorphic to its own direct summand?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2021 at 16:18 | comment | added | Mikhail Bondarko | It appears that Efimov always assumes certain finiteness conditions.(: | |
| Sep 6, 2021 at 12:07 | comment | added | Mikhail Bondarko | Thank you! I actually started from a $K_0$-formulation (no classes should vanish in it), but I did not read Efimov's paper.:) | |
| Sep 6, 2021 at 9:02 | comment | added | Evgeny Shinder | Such "Krull-Schmidt" type questions have an interpretation in terms of $K_0$ of the category of Chow motives about which very little is known. Some nontrivial tricks how to work with $K_0$ of an additive category are explained in Section 2 of Efimov's paper on L-equivalence arxiv.org/pdf/1707.08997.pdf. | |
| Sep 6, 2021 at 6:02 | comment | added | Mikhail Bondarko | Yet something like this may help in the setting I am interested in; thank you, Evgeny! | |
| Sep 5, 2021 at 22:06 | comment | added | Evgeny Shinder | One positive result is Lemma 1 in arxiv.org/pdf/0806.0173.pdf: it basically says that a motive with vanishing Chow groups over all field extensions is zero. However it is not sufficient for the positive answer to your question as Chow groups are infinite dimensional in general. | |
| Sep 5, 2021 at 18:05 | comment | added | Mikhail Bondarko | Yes, I am aware of this argument. And I am mostly interested in unconditional results and torsion coefficients. | |
| Sep 5, 2021 at 17:11 | history | asked | Mikhail Bondarko | CC BY-SA 4.0 |