特征零的限制性三分法
Restricted Trichotomy in Characteristic Zero
摘要：
证明了Zilber的限制性三分猜想的特征零情形。也就是说，我们表明，如果$\mathcal M$是任何非局部模强极小结构解释在一个代数闭域$K$的特征为零，然后$\mathcal M$本身解释$K$，特别是，任何非1为基础的结构解释在$K$是相互解释与$K$。值得注意的是，我们对待“一维”和“高维”的情况下的猜想，引入新的工具来解决高维的情况下，然后使用相同的工具来恢复以前已知的一维情况。
英文摘要：
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.
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