Iwasawa Theory for Artin Representations, I

Abstract

This article is the first of a pair of articles dealing with the Iwasawa theory of modular forms of weight 1 and, more generally, of Artin representations satisfying certain conditions. The main results in this part analyze the structure of certain Selmer groups for the Artin representation. In particular, it is shown that the Selmer groups are co-torsion as $\Lambda$-modules. For each Selmer group, we consider a generator of the characteristic ideal of its Pontrjagin dual. We call that the algebraic p-adic L-function. We also construct an analytic $p$-adic L-function via deformation to higher weights. Both of these $p$-adic L-functions should conjecturally have an interpolation property involving $p$-adic logarithms of global units analogous to Stark units. The proof of the interpolation property for the algebraic $p$-adic L-function will be given in Part 2 of this work.