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Zilber-Pink in a product of modular curves assuming multiplicative degeneration
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abstract
We prove the Zilber--Pink conjecture for curves in $Y(1)^n$ whose Zariski closure in $(\mathbb{P}^1)^n$ passes through the point $(\infty, \ldots, \infty)$, going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following Andr\'e's G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-archimedean places.
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Cited by 1 Pith paper
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G-functions, motives, and unlikely intersections -- old and new
A survey of the G-function method, its link to periods, and its use in proving cases of unlikely intersection conjectures.
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