Semi-stable models, local heights and quadratic Chabauty for $X_0(N{)}^{\ast }$

Nikola Adžaga, Maarten Derickx, Timo Keller

Quadratic Chabauty computations for $X_0(N{)}^{\ast }$ are complicated by local height contributions at primes of bad reduction. For squarefree $N$, we explain a strategy for constructing…