Junyi Xie

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math.AG2025

Arithmetic degree and its application to Zariski dense orbit conjecture

Yohsuke Matsuzawa, Junyi Xie

We prove that for a dominant rational self-map $f$ on a quasi-projective variety defined over $Q$ , there is a point whose $f$ -orbit is well-defined and its arit…

math.AG2025

Tate's question, Standard conjecture D, semisimplicity and Dynamical degree comparison conjecture

Fei Hu, Tuyen Trung Truong, Junyi Xie

Let $X$ be a smooth projective variety of dimension $n$ over the algebraic closure of a finite field $F_{p}$ . Assuming the standard conjecture $D$ , we prove a weaker form of…