6 problems

Let $N$ be a positive integer, let $L$ be the level-dependent integer used for the Galois action, and let $\mathcal{D}_N$ and $F_{m,h}$ be the indexing set and modular-unit basis i…

Let $N$ be a positive integer. Let $\mathscr{C}_N(\mathbf{Q})$ be the rational cuspidal subgroup of $J_0(N)$, and let $\mathscr{C}(N)$ be the rational cuspidal divisor class group…

Let $N$ be a positive integer. Let $X_0(N)$ be the modular curve of level $N$, let $J_0(N)$ be its Jacobian, and let $C_N(\mathbb{Q})$ be its rational cuspidal subgroup. Let $C(N)$…

Let $N$ be a positive integer. Let $C_N(\mathbb{Q})$ be the subgroup of $J_0(N)(\mathbb{Q})$ represented by degree-zero cuspidal divisors, and let $C(N)$ be the subgroup formed by…

Let $A$ be the ring of functions regular away from a fixed place at infinity, and let $\mathfrak n\lhd A$ be a non-zero square-free ideal. Let $X_0(\mathfrak n)$ be the smooth proj…

Let $p$ be a prime and $n$ a positive integer. For the cuspidal divisor class group $\mathscr C_1^\infty(p^n)$, let $[p]$ denote multiplication by $p$: … Define its $p$-rank to be…