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$\Kab$ has the Bogomolov property for canonical heights
We show that for any number field $K$ and any rational map $f$ in $K(x)$ that is not conjugate to a power, (signed) Chebyshev or Lattès map, then $K^{\mathrm{ab}}$ has the strong Bogomolov property for the canonical height of $f$. We also classify the pairs $(f,α)$ whose backward orbit contains infi
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