We prove a certain transcendence property of the unipotent Albanese map of a smooth variety, conditional on the Ax–Schanuel conjecture for variations of mixed Hodge structure. We show that this property allows the Chabauty–Kim method to be generalized to higher-dimensional varieties. In particular, we conditionally generalize several of the main Diophantine finiteness results in Chabauty–Kim theory to arbitrary number fields.

中文翻译：

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单能 Albanese 地图的功能超越

我们证明了平滑变体的单能 Albanese 映射的某种超越性，条件是混合霍奇结构变化的 Ax-Schanuel 猜想。我们表明，此属性允许 Chabauty-Kim 方法推广到更高维的变体。特别是，我们有条件地将 Chabauty-Kim 理论中的几个主要丢番图有限性结果推广到任意数域。