Green–Griffiths conjecture on algebraicity of normal-function zero loci

Let $\mathsf B$ be a complex algebraic manifold, let $\mathcal H$ be a variation of pure negative weight integral Hodge structures over $\mathsf B$, and let $\nu:\mathsf B\to\mathsf J(\mathcal H)$ be an admissible normal function, meaning a holomorphic section of the associated family of generalized intermediate Jacobians satisfying Griffiths horizontality and controlled asymptotic behavior near the boundary. Green–Griffiths conjecture. The zero locus of $\nu$ is algebraic. The conjecture concerns the algebraicity of loci defined by transcendental normal functions. It was proved in a series of papers, including for curves and then for arbitrary-dimensional bases, so the claim is solved.