Junyi Xie

activity

20232026

collaborators

8 papers

math.NT2026

Exceptional maps and abelian points in backward orbits

Zhuchao Ji, Jiarui Song, Junyi Xie

Consider a number field $K$ , a polarized endomorphism $f : X \to X$ on a normal projective variety, and a non-exceptional point $α$ for $f$ . We show that the extension $K(f^{-\infty}(…

math.NT2026

Faltings' Isogeny Theorem via Equidistribution

Junyi Xie, Ziquan Yang

We give a new proof of Faltings' isogeny theorem. More precisely, we show that Yuan's non-archimedean equidistribution theorem can be used to "pump" homomorphisms and semisimplicit…

math.DS2026

Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation

Zhuchao Ji, Junyi Xie

We prove the Gonality Conjecture in arithmetic dynamics: for any non-isotrivial one-parameter algebraic family of rational maps on $P_{C}^{1}$ , the gonality of dist…

math.NT2026

A geometric approach to the uniform boundedness of $ℓ$ -primary torsion points

Zhuchao Ji, Jiarui Song, Junyi Xie

We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we…

math.DS2025

Cyclotomic integral points for affine dynamics

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f : A^{N} \to A^{N}$ be a regular endomorphism of algebraic degree $d \geq 2$ (i.e., $f$ extends to an endomorphism on $P^{N}$ of algebraic degree $d$ ) defined…

math.AG2024

Numerical spectrums control Cohomological spectrums

Junyi Xie

Let $X$ be a smooth irreducible projective variety over a field $k$ of dimension $d .$ Let $τ : Q_{l} \to C$ be any field embedding. Let $f : X \to X$ be a surj…

math.CV2024

The moduli space of a rational map is Carathéodory hyperbolic

Zhuchao Ji, Junyi Xie

Let $f$ be a rational map of degree $d \geq 2$ . The moduli space $M_{f}$ , introduced by McMullen and Sullivan, is a complex analytic space consisting all quasiconformal conj…

math.DS2023

The multiplier spectrum morphism is generically injective

Zhuchao Ji, Junyi Xie

In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated…

Exceptional maps and abelian points in backward orbits

Faltings' Isogeny Theorem via Equidistribution

Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation

A geometric approach to the uniform boundedness of ℓ-primary torsion points

Cyclotomic integral points for affine dynamics

Numerical spectrums control Cohomological spectrums

The moduli space of a rational map is Carathéodory hyperbolic

The multiplier spectrum morphism is generically injective

A geometric approach to the uniform boundedness of $ℓ$ -primary torsion points