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Canonical heights and division polynomials
| Content Provider | Scilit |
|---|---|
| Author | de Jong, Robin Müller, J. Steffen |
| Copyright Year | 2014 |
| Description | We discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neitherp-adic nor complex analytic ones. In the case of genus 2 we also present a version that requires no factorisation at all. The method is based on a recurrence relation for the ‘division polynomials’ associated to hyperelliptic jacobians, and a diophantine approximation result due to Faltings. |
| Related Links | http://arxiv.org/pdf/1306.4030 http://arxiv.org/abs/1306.4030 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/AF24D793039C240073F6E55254C93106/S0305004114000371a.pdf/div-class-title-canonical-heights-and-division-polynomials-div.pdf |
| Ending Page | 373 |
| Page Count | 17 |
| Starting Page | 357 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004114000371 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 2 |
| Volume Number | 157 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2014-09-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Applied Mathematics Mathematical Physics Division Polynomials |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
