Zilber-Pink in a product of modular curves assuming multiplicative degeneration

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 $(\infty ,\dots ,\infty )$, going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following André's G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-archimedean places.

42 pages, corrected a few typos, CC BY licence applied in accordance with UKRI open access policy

Cited by in corpus (1)

• Some cases of the Zilber-Pink conjecture for curves in ${\mathcal{A}}_g$