On Dynamical Cancellation
On Dynamical Cancellation
复制标题
关于动态取消
DOI：
10.1093/imrn/rnac058
复制
发表时间：
2022
影响因子：
1
通讯作者：
Satriano Matthew
中科院分区：
文献类型：
--
作者：
Bell Jason P;Matsuzawa Yohsuke;Satriano Matthew
让be是一个射影簇，让be是一个显性自同态，两者都是在数域上定义的。我们考虑第二作者Meng、Shibata和Zhang的问题，他们问点塔$Y(K)\subseteq (f^{-1}(Y))(K)\subseteq (f^{-2}(Y))(K)\subseteq \cdots $最终是否稳定，其中是下的子品种不变量。当mapis étale时，我们表明这个问题有肯定的答案。我们还研究了一个相关的问题，即表明存在某个整数，仅依赖于 and ，这样无论何时，只要具有某些整数，我们就必然具有该属性。我们证明这对于射影簇的 etale 态射以及平滑射影曲线的自态射是成立的。我们还证明了多项式映射的更通用的消去定理，其中我们允许多个不同映射的组合。
Letbe a projective variety and letbe a dominant endomorphism of, both of which are defined over a number field. We consider a question of the 2nd author, Meng, Shibata, and Zhang, who asks whether the tower of-points $Y(K)\subseteq (f^{-1}(Y))(K)\subseteq (f^{-2}(Y))(K)\subseteq \cdots $ eventually stabilizes, whereis a subvariety invariant under. We show this question has an affirmative answer when the mapis étale. We also look at a related problem of showing that there is some integer, depending only onand, such that wheneverhave the property thatfor some, we necessarily have. We prove this holds for étale morphisms of projective varieties, as well as self-morphisms of smooth projective curves. We also prove a more general cancellation theorem for polynomial maps onwhere we allow for composition by multiple different maps.