论文标题
特征零的二分切开术
Restricted Trichotomy in Characteristic Zero
论文作者
论文摘要
我们证明了Zilber受限制的三分法猜想的特征零病例。也就是说，我们表明，如果$ \ MATHCAL M $是在特征零的代数封闭的$ k $中解释的任何非局部模块化最小的结构，则是$ \ Mathcal m $本身解释$ k $;特别是，以$ K $解释的任何基于1的非1基础结构都可以用$ k $来解释。值得注意的是，我们同时处理猜想的“一维”和“高维”案例，引入了新的工具来解决更高的案例，然后使用相同的工具来恢复先前已知的一维情况。
We prove the characteristic zero case of Zilber's Restricted Trichotomy Conjecture. That is, we show that if $\mathcal M$ is any non-locally modular strongly minimal structure interpreted in an algebraically closed field $K$ of characteristic zero, then $\mathcal M$ itself interprets $K$; in particular, any non-1-based structure interpreted in $K$ is mutually interpretable with $K$. Notably, we treat both the `one-dimensional' and `higher-dimensional' cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.
