Timeline for Which cases of Beilinson-Bloch-Kato for elliptic motives are known?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2021 at 9:38 | comment | added | David Loeffler | Morally yes, although there are some mildly fiddly technical issues meaning we don't have a full proof written out yet for Sym^3 of an elliptic curve. See arxiv.org/abs/2005.04786 for Sym^3 of modular forms of level 1 and big weight. | |
| Jan 6, 2021 at 1:20 | comment | added | David Corwin | Is it fair to say that $k=3$ would use something like Theorem D of arxiv.org/pdf/2003.05960.pdf? | |
| Dec 30, 2020 at 22:58 | comment | added | David Corwin | To add to the second bullet-point, it seems that $\operatorname{Sym}^2{h^1(E)}(1)$ is covered by arxiv.org/abs/1411.7661 under some mild assumptions when the curve is modular (known in general e.g., over $\mathbb{Q}$ or a real quadratic field). | |
| Sep 6, 2020 at 7:36 | comment | added | David Loeffler | I'd be happy to discuss this further but MO isn't really the place for extended conversations -- feel free to get in touch via my warwick.ac.uk email. | |
| Sep 6, 2020 at 2:48 | comment | added | David Corwin | Thanks! What about over an imaginary quadratic field? In one case, I have a specific curve of rank $0$, and I'm interested in it over imaginary quadratic fields over which it has rank $1$. If I can show it explicitly for $k=2,3$, that's really all I need. (But I'm also interested in other cases, e.g., for certain rank $1$ curves over $\mathbb{Q}$.) | |
| Sep 4, 2020 at 8:40 | history | edited | David Loeffler | CC BY-SA 4.0 |
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| Sep 4, 2020 at 8:11 | history | edited | David Loeffler | CC BY-SA 4.0 |
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| Sep 4, 2020 at 8:06 | history | answered | David Loeffler | CC BY-SA 4.0 |