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- W2259241017 abstract "A family $f_t(z)$ of polynomials over a number field $K$ will be called emph{subhomogeneous} if and only if $f_t(z)=F(z^e, t)$ for some binary homogeneous form $F(X, Y)$ and some integer $egeq 2$. For example, the family $z^d+t$ is subhomogeneous. We prove a lower bound on the canonical height, of the form [hat{h}_{f_t}(z)geq epsilon max{h_{mathsf{M}_d}(f_t), log|operatorname{Norm}mathfrak{R}_{f_t}|},] for values $zin K$ which are not preperiodic for $f_t$. Here $epsilon$ depends only on the number of places at which $f_t$ has bad reduction. For suitably generic morphisms $varphi:mathbb{P}^1to mathbb{P}^1$, we also prove an absolute bound of this form for $t$ in the image of $varphi$ over $K$ (assuming the $abc$ Conjecture), as well as uniform bounds on the number of preperiodic points (unconditionally)." @default.
- W2259241017 created "2016-06-24" @default.
- W2259241017 creator A5010807143 @default.
- W2259241017 date "2015-10-29" @default.
- W2259241017 modified "2023-09-27" @default.
- W2259241017 title "Canonical heights and preperiodic points for subhomogeneous families of polynomials" @default.
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- W2259241017 hasPublicationYear "2015" @default.
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