Timeline for algebraicity of Néron-Tate canonical height for Abelian varieties over global function fields
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Sep 30, 2014 at 19:22 | comment | added | David Holmes | Re. edit 2: you must be careful as the Poincare bundle does not in general extend over the whole Neron model, but only over the identity component. However, as long as you multiply your section by a suitable positive integer to get in the identity component, then I think the proposed equality holds. It should be in Moret-Bailly’s article in Asterisque 127 in the number field case; IIRC same proof works (more easily) in function field case. | |
| Dec 5, 2013 at 0:53 | comment | added | Joe Silverman | The canonical height is a sum of local heights. At the non-archimedean places, the local contribution is $r\log q$, where $r\in\mathbb{Q}$ and $q$ is the norm of the prime. So over a function field, the logarithmic canonical height is $r\log(n)$, and the exponential height is algebraic. For number fields, the contribution from the archimedean places are logs of absolute values of theta functions (more or less). For a further discussion of the number field case, see the answer that I just posted at mathoverflow.net/questions/56331/… | |
| Dec 4, 2013 at 19:31 | history | edited | user19475 | CC BY-SA 3.0 |
added 6 characters in body
|
| Dec 4, 2013 at 18:42 | history | edited | user19475 | CC BY-SA 3.0 |
added 354 characters in body
|
| Dec 4, 2013 at 18:28 | history | edited | user19475 |
edited tags
|
|
| Dec 4, 2013 at 18:20 | history | edited | user19475 | CC BY-SA 3.0 |
added 74 characters in body
|
| Dec 4, 2013 at 18:14 | comment | added | user19475 | Thanks. I have asked a question in the mentioned linked question/answer. | |
| Dec 4, 2013 at 17:35 | comment | added | Vesselin Dimitrov | It lies in $\mathbb{Q}$, basically by intersection theory on the Neron model. This is mentioned in ACL's answer to the question you link to. For elliptic curves, this is contained in Theorem 9.3 (due to Manin) in Silverman's Advanced Topics in the Arithmetic of Elliptic Curves. | |
| Dec 4, 2013 at 17:23 | history | asked | user19475 | CC BY-SA 3.0 |