Elementary module associated to Selmer group of Artin representation

The functional equation for the Selmer group for an Artin representation was studied by Greenberg [3, 5], Greenberg and Vatsal [6] and Majumdar and Panda [11]. We compare various Selmer groups for an Artin representation over a totally complex field. We establish a stronger version of the algebraic functional equation of the dual Selmer groups. We show that the equality holds not only for the characteristic ideal but also for the corresponding elementary modules without the assumption of Λ -cotorsionness of the Selmer group