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We introduce a “hybrid” conjecture which is a common generalisation of the André-Oort conjecture and the André-Pink-Zannier conjecture and we prove that it is a consequence of the Zilber-Pink conjecture. This extends a previous work of V. Aslanyan and C. Daw. We also show that our hybrid conjecture implies the Zilber-Pink conjecture for hypersurfaces contained in weakly special subvarieties.
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