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Minimally critical endomorphisms of P^N

· 2020 · math.NT · arXiv 2006.12869

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abstract

We study the dynamics of the map endomorphism of N-dimensional projective space defined by f(X)=AX^d, where A is a matrix and d is at least 2. When d>N^2+N+1, we show that the critical height of such a morphism is comparable to its height in moduli space, confirming a case of a natural generalization of a conjecture of Silverman.

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Heights and morphisms in number fields

math.NT · 2024-11-20 · conditional · novelty 8.0

Provides an explicit power-saving asymptotic for counting points by pullback height under morphisms between projective spaces over number fields.

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  • Heights and morphisms in number fields math.NT · 2024-11-20 · conditional · none · ref 16 · internal anchor

    Provides an explicit power-saving asymptotic for counting points by pullback height under morphisms between projective spaces over number fields.