Néron Tate Height

Beschreibung

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Beschreibung

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. n 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.On an elliptic curve, the Néron-Severi group is of rank one and has a unique ample generator, so this generator is often used to define the Néron Tate height, which is denoted h without reference to a particular line bundle. (However, the height that naturally appears in the statement of the Birch Swinnerton-Dyer conjecture is twice this height.) On abelian varieties of higher dimension, there need not be a particular choice of smallest ample line bundle to be used in defining the Néron Tate height.