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

Daw, C. ORCID: https://orcid.org/0000-0002-2488-6729 and Orr, M. (2025) Zilber-Pink in a product of modular curves assuming multiplicative degeneration. Duke Mathematical Journal, 174 (13). pp. 2877-2926. ISSN 1547-7398 doi: 10.1215/00127094-2025-0011

Abstract/Summary

We prove the Zilber–Pink conjecture for curves in Y(1)^n whose Zariski closure in (P^1)^n passes through the point (∞, . . . , ∞), 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.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/120717
Identification Number/DOI	10.1215/00127094-2025-0011
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Duke University Press
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