Some new cases of Zilber-Pink in Y(1)³

2025/10/10 by Daw, Christopher, Orr, Martin, Papas, Georgios · 1 citation
#11G18 #11G50 #14G22 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.09603

Abstract

We prove the Zilber-Pink conjecture for curves in Y(1)³ that intersect a modular curve in the boundary. We also give an unconditional result for points having few places of supersingular reduction. Both results are proved using the G-function method for unlikely intersections.

Citations

• On the v-adic values of G-functions I
• Zilber-Pink in Y(1)ⁿ: Beyond multiplicative degeneration
• The large Galois orbits conjecture under multiplicative degeneration
• Zilber-Pink in a product of modular curves assuming multiplicative degeneration
• Functional Transcendence of Periods and the Geometric André--Grothendieck Period Conjecture
• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• Equidistribution de sous-variétés spéciales et o-minimalité: André-Oort géométrique
• On a modular Fermat equation
• Théorème des périodes et degrés minimaux d'isogénies

Cited by

• On the v-adic values of G-functions II

Related

• Zilber-Pink in Y(1)ⁿ: Beyond multiplicative degeneration
• Zilber-Pink in a product of modular curves assuming multiplicative degeneration
• On a modular Fermat equation
• Modular Zilber-Pink for geometrically generic varieties
• Some cases of the Zilber-Pink conjecture for curves in A_g