Some new cases of Zilber-Pink in $Y(1{)}^3$

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 unlikely intersection points having few places of supersingular reduction where they are close to a fixed base point. Both results are proved using the G-functions method for unlikely intersections.

42 pages; comments welcome