Toric ranks and component groups of Jacobians of modular curves
Toric ranks and component groups of Jacobians of modular curves
Let $p\neq{2,3}$ be a prime number and let $\Gamma \subset \mathrm{SL}_{2}(\mathbb{Z})$ be a congruence subgroup with modular curve $X_{\Gamma}/K$ and Jacobian $J(X_{\Gamma})$. In this paper we give an explicit group-theoretic description of the semistable toric rank and component group of $J(X_{\Gamma})$ at the finite places of $K$ lying over $p$. …