论文标题
分区多项式的共同估值
Common valuations of division polynomials
论文作者
论文摘要
在此注释中，我们证明了在多项式之间的取消指数$ k_ {v，n} $的公式该公式与yabuta-voutier的结果相同，对于$ \ mathbb {q} _ {p} $有限扩展的情况下，对于非完美残留物领域的非标准Kodaira类型的情况。
In this note we prove a formula for the cancellation exponent $k_{v,n}$ between division polynomials $ψ_n$ and $ϕ_n$ 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 is identical with the result of Yabuta-Voutier for the case of finite extension of $\mathbb{Q}_{p}$ and generalizes to the case of non-standard Kodaira types for non-perfect residue fields.
