Charles's arithmetic conjecture for motivated normal-function zero loci

Let $F\subseteq\mathbb C$ be a subfield, and let $\nu$ be an algebraically $F$-motivated (respectively, $F$-motivated) normal function on a complex algebraic manifold, meaning that it arises from the corresponding cycle-theoretic construction with the relevant data defined over $F$. Charles's conjecture. The zero locus of $\nu$ is algebraic and defined over $F$. This is an arithmetic refinement of the Green–Griffiths algebraicity conjecture, asking that the zero locus retain the field of definition of the motivating data. The paper's abstract states that this conjecture is proved for normal functions arising from algebraically trivial cycle classes, so the claim is solved in the scope addressed by the paper.