Remarks on Kato's Euler systems for elliptic curves with additive reduction
Remarks on Kato's Euler systems for elliptic curves with additive reduction
复制标题
加藤椭圆曲线加约欧拉系统的评论
DOI：
10.1016/j.jnt.2019.09.011
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发表时间：
2020
影响因子：
0.7
通讯作者：
Kentaro Nakamura
中科院分区：
文献类型：
--
作者：
Chan-Ho Kim;Kentaro Nakamura
扩展以前的工作，良好的减少的情况下，我们提供了一个数值准则来验证大部分的“岩泽主要猜想没有p-adic L-功能”的椭圆曲线与添加剂减少在一个奇素数p在分圆Z p-扩展。我们还推导出相应的p-部分的Birch和Swinnerton-Dyer公式的秩为零的椭圆曲线从相同的数值准则。最后给出了一些具体的例子，并在附录中说明了我们对Kato欧拉方程组的选择。
Extending the former work for the good reduction case, we provide a numerical criterion to verify a large portion of the “Iwasawa main conjecture without p-adic L-functions” for elliptic curves with additive reduction at an odd prime p over the cyclotomic Z p-extension. We also deduce the corresponding p-part of the Birch and Swinnerton-Dyer formula for elliptic curves of rank zero from the same numerical criterion. We give some explicit examples at the end and specify our choice of Kato's Euler system in the appendix.