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

Takashi Hara; Tadashi Ochiai

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

Number Theory 2025-11-13 v4

Authors: Takashi Hara , Tadashi Ochiai

Abstract

For an algebraic Hecke character defined on a CM field $F$ of degree $2d$ , Katz constructed a $p$ -adic $L$ -function of $d+1+\delta_{F,p}$ variables in his innovative paper published in 1978, where $\delta_{F,p}$ 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 $d+1+\delta_{F,p}$ 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.

Keywords

$p$-adic $L$-function Iwasawa Main Conjecture Artin motive CM field Hecke character

Cite

@article{arxiv.2407.06983,
  title  = {On the $p$-adic $L$-function and Iwasawa Main Conjecture for an Artin motive over a CM field},
  author = {Takashi Hara and Tadashi Ochiai},
  journal= {arXiv preprint arXiv:2407.06983},
  year   = {2025}
}

Comments

43 pages, Title is changed a bit. Theorem 2.5 (and Theorem in Introduction) is renewed; we slightly modify Katz, Hida and Tilouine's measure and construct the p-adic Hecke L-function independent of auxiliary element delta. Correspondingly, the proof of Theorem 3.2 (construction and the interpolation formula of the p-adic Artin L-function) is revised

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

Abstract

Keywords

Cite

Comments

Related papers