Euler characteristic of the Selmer group attached to an Artin representation

Abstract

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.