The revised relative Manin–Mumford conjecture for semi-abelian schemes
The revised relative Manin–Mumford conjecture for semi-abelian schemes
Let be a semi-abelian scheme over , and let be an irreducible closed subvariety of dimension . Assume that is not contained in a proper special subvariety of . Define fiberwise as the union of algebraic subgroups of codimension greater than .
Revised relative unlikely-intersection conjecture. The intersection is not Zariski dense in .
Here special subvarieties include the additional subvarieties, such as Ribet sections, identified through the mixed Shimura classification. The source presents this as the revised version of Pink's relative conjecture.
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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