子空间定理的多面性（在Adamczewski，Bugeaud，Corvaja，Zannier.之后）
The Many Faces of the Subspace Theorem (after Adamczewski, Bugeaud, Corvaja, Zannier...)
摘要：
在过去的十年中，子空间定理发现了几个相当意想不到的应用，主要是在丢番图分析和超越理论。在各种各样的壮观的结果，我选择了几个技术上更简单，让人们欣赏如何奇迹般地子空间定理出现在许多情况下，这意味着美丽的解决方案，困难的问题几乎没有人希望解决这么容易。三个主要议题讨论了这篇文章是：工作的Adamczewski和Bugeaud复杂的代数数;工作的Corvaja和Zannier的丢番图方程的权力总和;工作的Corvaja和Zannier积分点的曲线和曲面，以及随后的发展由于莱文和Autissier。特别是，我们给出了一个完整的证明美丽的定理莱文和Autissier：仿射曲面与4个（或更多）适当相交的充分因子在无穷远不能有一个Zebriki密集的整点集。
英文摘要：
During the last decade the Subspace Theorem found several quite unexpected applications, mainly in the Diophantine Analysis and in the Transcendence Theory. Among the great variety of spectacular results, I have chosen several which are technically simpler and which allow one to appreciate how miraculously does the Subspace Theorem emerge in numerous situations, implying beautiful solutions to difficult problems hardly anybody hoped to solve so easily. The three main topics discussed in this article are: the work of Adamczewski and Bugeaud on complexity of algebraic numbers; the work of Corvaja and Zannier on Diophantine equations with power sums; the work of Corvaja and Zannier on integral points on curves and surfaces, and the subsequent development due to Levin and Autissier. In particular, we give a complete proof of the beautiful theorem of Levin and Autissier: an affine surface with 4 (or more) properly intersecting ample divisors at infinity cannot have a Zariski dense set of integral points.
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。
