  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.
