An equivariant $p$-adic Artin conjecture

Abstract

We formulate an equivariant version of Greenberg's $p$-adic Artin conjecture for smoothed equivariant $p$-adic Artin $L$-functions in the context of an arbitrary one-dimensional admissible $p$-adic Lie extension of a totally real number field. Using results of the author on the Wedderburn decomposition of the total ring of quotients of the Iwasawa algebra $\hat{I}›(\mathcal{G})$, we deduce validity of the conjecture in several interesting cases.

33 pages, v2: minor changes following referee's report