发帖
雷达卡
摘要翻译：
Faltings在他对Baker's Garden书的贡献中给出了在$\BBBP^2$上的不可约因子$D$的一族例子，其中$\BBBP^2\set-D$在远离有限多个位置的数环的任何给定局部化上只有有限多个整点。他还指出，在他的证明中使用的$\BBB p^2\set-d$和\'etale覆盖都没有嵌入半交换变体，因此他的例子不容易归结为关于这类子变体的已知结果。在这篇注记中，我们证明了Faltings的结果是如何直接从Evertse和Ferretti的一个定理得到的；因此，这些例子可以通过指出，如果一个人拉回到$\BBBP^2$\eTale的覆盖之外，然后在$D$的拉回中添加分量，那么一个人可以将补嵌入到一个半交换变体中，并对原始除数$D$获得有用的丢番图逼近结果。
---
英文标题：
《Transplanting Faltings' garden》
---
作者：
Paul Vojta
---
最新提交年份：
2009
---
分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
--
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
---
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 \'etale 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 $\Bbb P^2$ \'etale 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 $D$.
---
PDF链接：
https://arxiv.org/pdf/0901.2106
京公网安备 11010802022788号
