阿廷表示对应的塞尔姆群的欧拉示性数
Euler characteristic of the Selmer group attached to an Artin representation
AI总结：
本文遵循Greenberg与Vatsal的框架，将Longo和Vigni推广Greenberg所得的p进伽罗瓦表示相关塞尔姆群基数关系，拓展至阿廷表示的情形。
AI中文摘要：
Longo和Vigni推广了Greenberg的结果，给出了p进伽罗瓦表示的分圆ℤₚ扩张上塞尔姆群的基数与其庞特里亚金对偶的特征幂级数之间的关系。本文遵循Greenberg和Vatsal的框架，将该结果推广到阿廷表示的情形。
英文摘要：
Longo and Vigni extended a result of Greenberg by giving a relation between the cardinality of the Selmer group and the characteristic power series of its Pontryagin dual over the cyclotomic $\mathbb{Z}_p$-extension for a $p$-adic Galois representation. In this paper, we extend this result to the case of Artin representations, following the framework of Greenberg and Vatsal.
