Patrick Ingram
Published 2016-10-25Version 1
The critical height of a rational function (with algebraic coefficients) is a natural measure of dynamical complexity, essentially an adelic analogue of the Lyapunov exponent. Coordinate-free, it is well-defined on moduli space, but bears no obvious relation to the arithmetic geometry of that space as a variety. At a conference in 2010, Silverman conjectured that this disconnect is superficial, and that in fact the critical height should be at least commensurate to any ample Weil height on the moduli space, except on the Lattes locus (where that has no hope of being true). Here, we prove that conjecture.
Moduli spaces for families of rational maps on P^1
The $p$-rank stratification of the moduli space of double covers of a fixed elliptic curve
Integrality properties in the Moduli Space of Elliptic Curves: Isogeny Case
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