论文标题
另一个看模块化雅各布人的理性扭转
Another look at rational torsion of modular Jacobians
论文作者
论文摘要
我们研究了每平方英尺的$ n $ $ n $ jacobian $ j_0（n）$的理性扭转子组。我们给出了OHTA结果的新证明，该结果是OGG猜想的概括：对于素数$ p \ nmid 6n $，$ p $ - 理性扭转亚组的主要部分等同于cuspidal子组的部分。尽管以前对此结果的证据使用了这些组的基础性的明确计算，但我们将它们的结构用作Hecke代数的模块。
We study the rational torsion subgroup of the modular Jacobian $J_0(N)$ for $N$ a square-free integer. We give a new proof of a result of Ohta on a generalization of Ogg's conjecture: for a prime number $p \nmid 6N$, the $p$-primary part of the rational torsion subgroup equals that of the cuspidal subgroup. Whereas previous proofs of this result used explicit computations of the cardinalities of these groups, we instead use their structure as modules for the Hecke algebra.
