Modular Zilber–Pink conjecture, optimal version
Modular Zilber–Pink conjecture, optimal version
Let be a positive integer and let be an algebraic variety. For a subvariety , define its defect by
The subvariety is optimal in if every subvariety with satisfies , and denotes the set of all optimal subvarieties of . Modular Zilber–Pink conjecture, optimal version. The set is finite. This is a formulation in terms of optimal subvarieties, which generalize maximal atypical components; its resolution is not specified in the source.
Sources & referencesView supporting material
Primary source
Vahagn Aslanyan, Sebastian Eterović and Guy Fowler, “Modular Zilber-Pink for geometrically generic varieties”, arXiv:2509.03160 (2025).
Additional references
4 papers in this index state this conjecture (2018–2025). The statement above is taken from the most recent of them; the others are arXiv:2209.12192, arXiv:1803.04753, arXiv:1803.05895.
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