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Local Height Functions

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Part of the Graduate Texts in Mathematics book series (GTM, volume 151)

Abstract

The canonical height function
$$ \hat{h}:E\left( {\bar{K}} \right) \to \left[ {0,\infty } \right) $$
is a quadratic form whose value at a point P measures the arithmetic complexity of P. The importance of the canonical height stems from the fact that it relates the geometrically defined group law to the arithmetic properties of the algebraic points on E. See [AEC VIII, §91 for details].

Keywords

Elliptic Curve Height Function Good Reduction Finite Extension Bounded Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

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