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We introduce a ``hybrid'' conjecture which is a common generalisation of theAndr\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture and we provethat it is a consequence of the Zilber-Pink conjecture. We also show that ourhybrid conjecture implies the Zilber-Pink conjecture for hypersurfacescontained in weakly special subvarieties.

A Common Generalisation of the Andr\'e-Oort and Andr\'e-Pink-Zannier Conjectures