论文标题
有理图上有常规迭代的emiabelian品种
Rational self-maps with a regular iterate on a semiabelian variety
论文作者
论文摘要
让$ g $为在代数封闭的特征$ 0 $ 0 $的代数封闭场上定义的Semiabelian品种。令$φ\ colon g \ dashrightarrow g $为主要的理性自我图。假设迭代$φ^m \ colon g \ to g $对于某些$ m \ geqslant 1 $是常规的，并且没有非恒定同构$τ：g \ g \ g_0 $ semiabelian品种，因此$τ\τ\ circcim k k} = m k} =τ$ k for Some $ K for Some $ k \ geqs。我们表明，在这些假设下，$φ$本身必须是常规的。我们还证明了这一主张的一种主要特征和现有示例，表明我们的结果很清晰。
Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of characteristic $0$. Let $Φ\colon G\dashrightarrow G$ be a dominant rational self-map. Assume that an iterate $Φ^m \colon G \to G$ is regular for some $m \geqslant 1$ and that there exists no non-constant homomorphism $τ: G\to G_0$ of semiabelian varieties such that $τ\circ Φ^{m k}=τ$ for some $k \geqslant 1$. We show that under these assumptions $Φ$ itself must be a regular. We also prove a variant of this assertion in prime characteristic and present examples showing that our results are sharp.
