The revised relative Manin–Mumford conjecture in torsion-point form
Let be a semi-abelian scheme of relative dimension with toric rank , and let be an irreducible variety over . Let be an irreducible closed subvariety of , dominant over . Write for the fiberwise torsion points.
Revised relative Manin–Mumford conjecture. If is Zariski dense in , then either is contained in a special subvariety of , or .
The source calls this an immediate corollary of the revised relative conjecture. It is proposed after the original formulation is shown to fail because of Ribet sections.
References
Primary source
Kaiyuan Gu and Chenxin Huang, “On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures”, arXiv:2410.17755 (2024).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.