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

2024/07/09 by Hara, Takashi, Ochiai, Tadashi
#11G15 #11L05 #11R23 (Primary) #11R42 (Secondaries) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.06983

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. 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+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. 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.

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