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Computing Néron–Tate heights of points on hyperelliptic Jacobians
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Holmes, David. (2012) Computing Néron–Tate heights of points on hyperelliptic Jacobians. Journal of Number Theory, Vol.132 (No.6). pp. 1295-1305. ISSN 0022-314X
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Official URL: http://dx.doi.org/10.1016/j.jnt.2012.01.002
Abstract
t was shown by Faltings (1984) [Fal84] and Hriljac (1985) [Hri85] that the Néron-Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it to give an algorithm for computing Néron-Tate heights on Jacobians of (hyper)elliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing Néron-Tate heights on Jacobians of (hyper)elliptic curves of genus 1 ≤ g≤ 9. © 2012 Elsevier Inc..
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Number Theory |
| Publisher: | Academic Press |
| ISSN: | 0022-314X |
| Date: | June 2012 |
| Volume: | Vol.132 |
| Number: | No.6 |
| Page Range: | pp. 1295-1305 |
| Identification Number: | 10.1016/j.jnt.2012.01.002 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/47011 |
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