On the 𝑝-adic 𝐿-function and Iwasawa main conjecture for an Artin motive over a CM field

Abstract

For an algebraic Hecke character defined on a CM field 𝐹 of degree 2𝑑, Katz constructed a 𝑝-adic 𝐿-function of 𝑑 + 1 + 𝛿_𝐹,𝑝 variables in his innovative paper published in 1978, where 𝛿_𝐹,𝑝 denotes the Leopoldt defect for 𝐹 and 𝑝. We shall generalise the result of Katz under several technical conditions (containing the absolute unramifiedness of 𝐹 at 𝑝), and construct a 𝑝-adic Artin 𝐿-function of 𝑑 + 1 + 𝛿_𝐹,𝑝 variables, which interpolates critical values of the Artin 𝐿-function associated to a 𝑝-unramified Artin representation of the absolute Galois group 𝐺_𝐹 of 𝐹. Our construction is an analogue over a CM field of Greenberg's construction over a totally real field, but there appear new difficulties which do not matter in Greenberg's case.