Canonical heights and division polynomials

Abstract

AbstractWe 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.