p-adic L-function and Iwasawa Main Conjecture for an Artin motive over a CM field

For an algebraic Hecke character defined on a CM field F of degree 2d, Katz constructed a p-adic L-function of d+1+₅, ₏ variables in his innovative paper published in 1978, where ₅, ₏ denotes the Leopoldt defect for F and p. In the present article, we 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+₅, ₏ variables, which interpolates critical values of the Artin L-function associated to a p-unramified Artin representation of the absolute Galois group GF. 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.