= Canonical height pairing
{title2=$\langle P,Q\rangle=\tfrac12(\widehat h(P+Q)-\widehat h(P)-\widehat h(Q))$}
The canonical height pairing is $\langle P,Q\rangle=(\widehat h(P+Q)-\widehat h(P)-\widehat h(Q))/2$. The <height parallelogram identity> makes it bilinear. It descends through torsion and is positive definite on the free part of the <Mordell-Weil group>. The <Cauchy-Schwarz inequality> gives $\widehat h(P-Q)\leq2\widehat h(P)+2\widehat h(Q)$, useful for height descent.
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