Work

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

Year: 2025

Type: article

Abstract: We prove the Zilber–Pink conjecture for curves in Y(1)n whose Zariski closure in (P1)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.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2025-0011

Authors: Christopher Daw, Martin Orr

Institutions: University of Reading, University of Manchester

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: G1541836534, Quantitative reduction theory and Diophantine geometry, G8019455772, Problems of Unlikely Intersections: The Zilber-Pink Conjecture for Shimura varieties