Iwasawa theory for Artin representations I

<!-- *** Custom HTML *** --> We introduce a natural way to define Selmer groups and p-adic L-functions for modular forms of weight 1. The corresponding Galois representation ρ of Gal(Q̄/Q) is a 2-dimensional Artin representation with odd determinant. Thus, the dimension d⁺ of the (+1)-eigenspace for complex conjugation is 1. Choose a prime p such that the restriction of ρ to the local Galois group Gal(Q̄ₚ/Qₚ) has a 1-dimensional constituent ε with multiplicity 1. If we fix the choice of such an ε, we can define a Selmer group and a p-adic L-function. On the algebraic side, we prove that the Selmer group over the cyclotomic Zₚ-extension of Q is a cotorsion module over the Iwasawa algebra Λ. That result is valid for an Artin representation of arbitrary dimension d under the assumption that d⁺ = 1 and that such an ε can be chosen. On the analytic side, the corresponding complex L-function has no critical values and the definition of the p-adic L-function depends on deforming the Galois representation ρ by Hida theory.