On p-adic Artin L-functions II

Let p be a prime. Iwasawa’s famous conjecture relating Kubota-Leopoldt p-adic L-functions to the structure of certain Galois groups has been proven by Mazur and Wiles in [10]. Wiles later proved a far-reaching generalization involving p-adic L-functions for Hecke characters of finite order for a totally real number field in [14]. As we discussed in [5], an analogue of Iwasawa’s conjecture for p-adic Artin L-functions can then be deduced. The formulation again involves certain Galois groups. However, one can reformulate this result in terms of Selmer groups for the Artin representations. There are several advantages to such a reformulation. First of all, it fits perfectly into the much broader framework described in [6] which relates the p-adic L-function for a motive to the corresponding Selmer group. The crucial assumption in [6] that the motive be ordinary at p (or at least potentially ordinary) is satisfied by an Artin motive and all of its Tate twists. A second advantage of a reformulation involving Selmer groups is that the issue of how to define the μ-invariant becomes resolved in a natural and transparent way. Thirdly, the arguments in [5] can be simplified. In particular, there is no need for singling out the class of Artin representations which are called type S in [5]. The purpose of this paper is to explain these advantages. Suppose that F is a totally real number field. Consider an Artin representation