Néron–Tate height

In number theory, the Néron–Tate height (or canonical height) is a quadratic form on the Mordell-Weil group of rational points of an abelian variety defined over a global field. It is named after André Néron and John Tate.

Néron defined the Néron–Tate height as a sum of local heights. Although the global Néron–Tate height is quadratic, the constituent local heights are not quite quadratic. Tate (unpublished) defined it globally by observing that the logarithmic height ${\displaystyle h_{L}}$ associated to a symmetric invertible sheaf ${\displaystyle L}$ on an abelian variety ${\displaystyle A}$ is “almost quadratic,” and used this to show that the limit

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