Journal of the Ramanujan Mathematical Society

Volume 39, Issue 2, June 2024 pp. 109–129.

On characteristic ideal of Selmer group associated to Artin representations

Authors: Dipramit Majumdar and Subhasis Panda
Author institution:Department of Mathematics, Indian Institute of Technology Madras, IIT P.O. Chennai 600 036, India.

Summary: Selmer group for an Artin representation over totally real fields was studied by Greenberg [Gr1,Gr5] and Vatsal [Va]. In this paper we study the Selmer group for an Artin representation over a totally complex field. We establish an algebraic functional equation of the characteristic ideal of the dual 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.

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