Arithmetic intersections on non-split Cartan modular curves

Jonathan Love, Elie Studnia, Jan Vonk

Let $p$ be a prime number, and let ${\Delta }_1,{\Delta }_2<0$ be two coprime fundamental discriminants. When $p$ splits in $\mathbb{Q}(\sqrt{{\Delta }_1})$ and $\mathbb{Q}(\sqrt{{\Delta }_2})$ the height pairi…