(transcendence of canonical heights)
Is the Néron-Tate canonical height for an Abelian variety $A$ over a global function field $K$, $\hat{h}: A(K) \times A^\vee(K) \to \mathbf{R}$ known to always lie in $\bar{\mathbf{Q}}$?
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algebraicity of Néron-Tate canonical height for Abelian varieties over global function fields
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