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Functional transcendence for the unipotent Albanese map
Algebra & Number Theory  (IF0.938),  Pub Date : 2021-10-16, DOI: 10.2140/ant.2021.15.1565
Daniel Rayor Hast

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.