Timeline for Chow Groups of varieties over number fields
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2018 at 11:29 | comment | added | Watson | It is stated as Swinnerton-Dyer conjecture in Beilinson's Height pairings between algebraic cycles (conjecture 5.0). | |
| Dec 16, 2017 at 18:48 | answer | added | guest | timeline score: 4 | |
| Dec 16, 2017 at 13:37 | answer | added | Lucifer | timeline score: 7 | |
| Dec 16, 2017 at 8:51 | answer | added | David Loeffler | timeline score: 12 | |
| Dec 16, 2017 at 6:21 | comment | added | user19475 | I have found math.clemson.edu/~jimlb/ConferenceTalks/PCMI2009/kings.pdf p. 8 and 9. | |
| Dec 16, 2017 at 3:06 | history | edited | gdb |
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| Dec 16, 2017 at 3:03 | comment | added | R. van Dobben de Bruyn | @gdb my thoughts as well. Although I think the same is conjectured over finite fields, where we also don't know anything. In that case it really does seem to follow from Bass. | |
| Dec 16, 2017 at 2:59 | comment | added | gdb | @Mohan I think that Bass conjecture is not precisely the same conjecture as one I am asking about. The reason is that varieties over number fields are not schemes of finite type over $\mathbf Z$. And I am not sure how spreading out techniques work for $K$-theory/Chow groups. | |
| Dec 16, 2017 at 2:50 | history | edited | gdb | CC BY-SA 3.0 |
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| Dec 16, 2017 at 2:34 | comment | added | Mohan | For any smooth variety $X$, you have a filtration $\{F^iK_0(X)\}$ of the $K_0$ and natural identification of $F^i/F^{i+1}\otimes \mathbb{Q}$ with $CH^i(X)\otimes\mathbb{Q}$, by Grothendieck Rieman-Roch without denominators. So, Bass conjecture for $K_0$ is equivalent to what you ask. I do not know how much is known for either. | |
| Dec 16, 2017 at 1:37 | comment | added | R. van Dobben de Bruyn | This might be related to Bass's conjecture. I am not really an expert, though. | |
| Dec 16, 2017 at 1:07 | history | edited | gdb | CC BY-SA 3.0 |
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| Dec 16, 2017 at 0:57 | history | asked | gdb | CC BY-SA 3.0 |