On the nonvanishing of generalised Kato classes for elliptic curves of rank 2
On the nonvanishing of generalised Kato classes for elliptic curves of rank 2
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关于2阶椭圆曲线的广义Kato类的不消失性
DOI：
10.1017/fms.2021.85
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Hsieh, Ming-Lun
中科院分区：
文献类型：
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作者：
Castella, Francesc;Hsieh, Ming-Lun
设为一条椭圆曲线，是E的一个普通素数，它的根数是so。当辅助特征形g具有复乘法时，我们证明了关于辅助特征形g具有复乘法时的第一种情况。特别地，给出了二阶椭圆曲线的非平凡Selmer类的一种新构造。
Let be an elliptic curve and be a good ordinary prime for E and assume that with root number (so ). A construction of Darmon–Rotger attaches to E and an auxiliary weight 1 cuspidal eigenform g such that , a Selmer class , and they conjectured the equivalence In this article, we prove the first cases on Darmon–Rotger’s conjecture when the auxiliary eigenform g has complex multiplication. In particular, this provides a new construction of nontrivial Selmer classes for elliptic curves of rank 2.