Zilber-Pink in $Y(1)^n$: Beyond multiplicative degeneration

Georgios Papas

Zilber-Pink in $Y(1)^n$: Beyond multiplicative degeneration

Number Theory 2026-02-23 v2 Algebraic Geometry

Authors: Georgios Papas

Abstract

We establish Large Galois orbits conjectures for points of unlikely intersections of curves in $Y(1)^n$ , upon assumptions on the intersection of such curves with the boundary $X(1)^n\backslash Y(1)^n$ , in the Zilber-Pink setting. As a corollary, building on work of Habegger-Pila and Daw-Orr, we obtain new cases of the Zilber-Pink conjecture for curves in $Y(1)^n$ .

Keywords

Zilber-Pink conjecture unlikely intersections Galois orbits curves $Y(1)^n$ modular curves

Cite

@article{arxiv.2402.09487,
  title  = {Zilber-Pink in $Y(1)^n$: Beyond multiplicative degeneration},
  author = {Georgios Papas},
  journal= {arXiv preprint arXiv:2402.09487},
  year   = {2026}
}

Comments

This content formerly appeared in arXiv:2310.04943v1, which has been split into two papers. Version accepted for publication by the Israel Journal of Mathematics

Zilber-Pink in $Y(1)^n$: Beyond multiplicative degeneration

Abstract

Keywords

Cite

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