Functional transcendence for the unipotent Albanese map
Number Theory
2021-10-20 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1911.00587,
title = {Functional transcendence for the unipotent Albanese map},
author = {Daniel Rayor Hast},
journal= {arXiv preprint arXiv:1911.00587},
year = {2021}
}
Comments
14 pages