Abstract
In this note, we prove a formula for the cancellation exponent
$k_{v,n}$
between division polynomials
$\psi _n$
and
$\phi _n$
associated with a sequence
$\{nP\}_{n\in \mathbb {N}}$
of points on an elliptic curve
$E$
defined over a discrete valuation field
$K$
. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.
Publisher
Cambridge University Press (CUP)