The revised relative Manin–Mumford conjecture in torsion-point form
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.
Sources & referencesView supporting material
Primary source
Kaiyuan Gu and Chenxin Huang, “On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures”, arXiv:2410.17755 (2024).
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