Timeline for Is Ш a good parameter for the failure of Global-Local principle for abelian varieties?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2016 at 16:30 | history | edited | Myshkin | CC BY-SA 3.0 |
+ top level tag (ag.), ECs and arith. geom.
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| Apr 6, 2015 at 17:24 | vote | accept | Donggeon Yhee | ||
| Apr 6, 2015 at 17:24 | |||||
| Apr 6, 2015 at 11:14 | answer | added | Chris Wuthrich | timeline score: 2 | |
| Apr 6, 2015 at 3:07 | comment | added | Yemon Choi | @ChrisWuthrich I've cast the final vote to re-open, so I suggest you turn your comments into an answer | |
| Apr 6, 2015 at 3:06 | history | reopened |
Joonas Ilmavirta Dima Pasechnik Daniel Loughran Alex Degtyarev Yemon Choi |
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| Apr 4, 2015 at 20:32 | comment | added | Chris Wuthrich | Sorry for the chain of comments, but the question is not (yet ?) open for an answer. | |
| Apr 4, 2015 at 20:32 | comment | added | Chris Wuthrich | There is some evidence that the fine Sha is much smaller. For instance even over infinite extension considered in Iwasawa theory the fine Sha should be finite (all the time ?) while the full Sha can get very large. | |
| Apr 4, 2015 at 20:29 | comment | added | Chris Wuthrich | As to the kernel of your map: This is what I would call the "fine Tate-Shafarevich group". There are examples of when it is trivial, half or all of the Tate-Shafarevich group when the latter has 4 elements. In general I would think the kernel could just be anything. Proc. Camb. Soc. 142 (2007), no. 1, p. 1-12. | |
| Apr 4, 2015 at 11:23 | history | edited | Donggeon Yhee | CC BY-SA 3.0 |
added 3 characters in body
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| Apr 4, 2015 at 11:10 | history | edited | Donggeon Yhee | CC BY-SA 3.0 |
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| Apr 3, 2015 at 19:09 | comment | added | Chris Wuthrich | (After edit): Take $\ell$-primary parts everywhere. Then the local product of the first term is just $E(\mathbb{Q}_{\ell})\otimes\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell}$ which is cofree of rank $1$. So $\operatorname{coker}(a)[\ell^{\infty}]$ is finite if the rank of $E(\mathbb{Q})$ is positive and is cofree of corank $1$ otherwise. That does not look analogous to your huge local product in $r$. | |
| Apr 2, 2015 at 13:58 | review | Reopen votes | |||
| Apr 6, 2015 at 3:07 | |||||
| Apr 2, 2015 at 13:40 | history | edited | Donggeon Yhee | CC BY-SA 3.0 |
added 1115 characters in body
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| Apr 2, 2015 at 8:25 | history | closed |
Daniel Loughran Joonas Ilmavirta Stefan Kohl♦ Alex Degtyarev abx |
Needs details or clarity | |
| Apr 1, 2015 at 20:48 | review | Close votes | |||
| Apr 2, 2015 at 8:25 | |||||
| Apr 1, 2015 at 15:28 | comment | added | Chris Wuthrich | And the title of the question als odoes not seem to have much relation to the question itself. | |
| Apr 1, 2015 at 15:25 | comment | added | Chris Wuthrich | What is your definition of $Sel(E/\mathbb{Q})$ ? My first guess would be the inductive limit of $n$-Selmer groups. But then I can't see how you defined the map you want to be injective. Did you mean the target to be $E(\mathbb{Q}_p)\otimes \mathbb{Q}/\mathbb{Z}$ ? I think this question needs some improvement to be understandable. | |
| Apr 1, 2015 at 15:22 | history | undeleted | Donggeon Yhee | ||
| Apr 1, 2015 at 15:22 | history | deleted | Donggeon Yhee | via Vote | |
| Apr 1, 2015 at 15:06 | history | asked | Donggeon Yhee | CC BY-SA 3.0 |