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引用次数: 7
摘要
受N. P. Smart方法的启发，我们描述了一种算法来确定$\mathbb{Q}$上的所有Picard曲线，这些曲线从3到$\mathbb{Q}$ -同构都很好。建立了此类曲线的同构类与具有有理线性因子的某些五次二元形式的对应关系。给出了一组完整的积分模型，并讨论了其在Ihara问题上的应用。
Picard curves over Q with good reduction away from 3
Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over $\mathbb{Q}$
with good reduction away from 3, up to $\mathbb{Q}$
-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined and an application to a question of Ihara is discussed.
期刊介绍：
LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.
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