Diophantine Geometry: An Introduction
《Diophantine Geometry: An Introduction》 · 第 238–239 页 · Section B.8「Local Height Functions」，Theorem B.8.1
For a smooth projective variety $V/k$ and $D\in\operatorname{Div}(V)$, the local height machine assigns a function $\lambda_D:\coprod_{v\in M_k}V_D(k_v)\to\mathbb R$, called the local height function with respect to $D$, with normalization, additivity, functoriality, positivity, and local/global properties.