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arXiv · 2401.03528

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

Rodolphe Richard·Andrei Yafaev
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Abstract

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

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Rodolphe Richard, Andrei Yafaev. 2024-01-07. A Common Generalisation of the Andr\'e-Oort and Andr\'e-Pink-Zannier Conjectures. https://arxiv.org/abs/2401.03528

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