Canonical heights and division polynomials
| Autor: | Robin de Jong, J. Steffen Müller |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Recurrence relation Mathematics - Number Theory General Mathematics Mathematics::Number Theory 11G10 11G30 11G50 14H40 14H45 Algebraic number field Diophantine approximation symbols.namesake Mathematics::Algebraic Geometry Factorization Genus (mathematics) Jacobian matrix and determinant symbols FOS: Mathematics Number Theory (math.NT) Algebraic number Division polynomials Mathematics |
| Zdroj: | Mathematical Proceedings of the Cambridge Philosophical Society, 157(2), 357-373 |
| Popis: | 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, neither $p$-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. Comment: 17 pages, 2 figures, 2 tables; comments welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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