论文标题
关于与Artin表示相关的Selmer群体的特征理想
On characteristic ideal of Selmer group associated to Artin representations
论文作者
论文摘要
格林伯格（Greenberg）和瓦萨尔（Vatsal）研究了Selmer Group for Artin of Attry Real领域的代表。在本文中，我们研究了Selmer小组在一个完全复杂的领域中的ARTIN代表。我们建立了与Artin表示相关的Selmer组的特征理想的代数函数，而在某些轻度假设下，有理数数字扩展了合理数字的扩展，并构建了几个示例以说明我们的结果。我们还证明，在这种情况下，双Selmer集团的$ $ $ invariant与晶格的选择无关。
Selmer group for an Artin representation over totally real fields was studied by Greenberg and Vatsal. In this paper we study the Selmer groups for an Artin representation over a totally complex field. We establish an algebraic function of the characteristic ideal of the Selmer group associated to Artin representation over the cyclotomic $\Z_p$- extension of the rational numbers under certain mild hypotheses and construct several examples to illustrate our result. We also prove that in this situation $μ$-invariant of the dual Selmer group is independent of the choice of the lattice.
