Junyi Xie

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20232026

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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…

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

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