On characteristic ideal of Selmer group associated to Artin representations

TL;DR

This paper investigates the algebraic properties of Selmer groups linked to Artin representations over totally complex fields, extending prior work and establishing new invariants and examples in Iwasawa theory.

Contribution

It establishes a formula for the characteristic ideal of Selmer groups for Artin representations over cyclotomic extensions and shows the independence of the μ-invariant from lattice choices.

Findings

Derived an algebraic function for the characteristic ideal.

Constructed examples illustrating the main theorem.

Proved μ-invariant independence from lattice choice.

Abstract

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 $\mu$-invariant of the dual Selmer group is independent of the choice of the lattice.