Details

Autor(en) / Beteiligte

• Yoo, Hwajong

Titel

On rational Eisenstein primes and the rational cuspidal groups of modular Jacobian varieties

Ist Teil von

• Transactions of the American Mathematical Society, 2019-08, Vol.372 (4), p.2429-2466

Erscheinungsjahr

2019

Quelle

American Mathematical Society Journals

Beschreibungen/Notizen

• Let N be a non-squarefree positive integer and let \ell be an odd prime such that \ell ^2 does not divide N. Consider the Hecke ring \mathbb{T}(N) of weight 2 for \Gamma _0(N) and its rational Eisenstein primes of \mathbb{T}(N) containing \ell . If \mathfrak{m} is such a rational Eisenstein prime, then we prove that \mathfrak{m} is of the form (\ell , ~\mathcal {I}^D_{M, N}), where we also define the ideal \mathcal {I}^D_{M, N} of \mathbb{T}(N). Furthermore, we prove that \mathcal {C}(N)[\mathfrak{m}] \neq 0, where \mathcal {C}(N) is the rational cuspidal group of J_0(N). To do this, we compute the precise order of the cuspidal divisor \mathcal {C}^D_{M, N} and the index of \mathcal {I}^D_{M, N} in \mathbb{T}(N)\otimes \mathbb{Z}_\ell .