移植Faltings花园
Transplanting Faltings' garden
摘要：
在他的贡献贝克的花园书，法尔明斯给出了一个家庭的例子不可约因子$D$对$\Bbb P^2$的$\Bbb P^2\setminus D$只有1000多个积分点超过任何给定的本地化的一个数环远离1000多个地方。他还指出，无论是$\Bbb P^2\setminus D$还是他的证明中使用的étale覆盖嵌入到半阿贝尔品种，所以他的例子不容易减少到已知的结果，这样的子品种。在这篇文章中，我们展示了如何直接从Evertse和Ferretti的一个定理中得出Faltings的结果;因此这些例子可以解释为，如果一个人拉回到$D$之外的$\Bbb P^2$的覆盖，然后将分量添加到$D$的拉回中，那么就可以将补集嵌入到半阿贝尔簇中，并为原始除数$D$获得有用的丢番图逼近结果。
英文摘要：
In his contribution to the Baker's Garden book, Faltings gives a family of examples of irreducible divisors $D$ on $\Bbb P^2$ for which $\Bbb P^2\setminus D$ has only finitely many integral points over any given localization of a number ring away from finitely many places. He also notes that neither $\Bbb P^2\setminus D$ nor the étale covers used in his proof embed into semiabelian varieties, so his examples do not easily reduce to known results about such subvarieties. In this note, we show how Faltings' results follow directly from a theorem of Evertse and Ferretti; hence these examples can be explained by noting that if one pulls back to a cover of $\Bbb P^2$ étale outside of $D$ and then adds components to the pull-back of $D$ then one can embed the complement into a semiabelian variety and obtain useful diophantine approximation results for the original divisor $D$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
