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arXiv · 1911.00587

Functional transcendence for the unipotent Albanese map

Daniel Rayor Hast
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Abstract

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.

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Daniel Rayor Hast. 2021-01-02. Functional transcendence for the unipotent Albanese map. https://doi.org/10.2140/ant.2021.15.1565

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