Silverman defined the critical height of a rational function of degree in terms of the asymptotic rate of growth of the Weil height along the critical orbits of . He also conjectured that this quantity was commensurate to an ample Weil height on the moduli space of rational functions degree . We prove that conjecture.
"The critical height is a moduli height." Duke Math. J. 167 (7) 1311 - 1346, 15 May 2018. https://doi.org/10.1215/00127094-2017-0053