{
  "id": "2407.06983",
  "version": "v1",
  "published": "2024-07-09T15:57:52.000Z",
  "updated": "2024-07-09T15:57:52.000Z",
  "title": "$p$-adic $L$-function and Iwasawa Main Conjecture for an Artin motive over a CM field",
  "authors": [
    "Takashi Hara",
    "Tadashi Ochiai"
  ],
  "comment": "38 pages",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T15:57:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F41",
      "11F67"
    ],
    "keywords": [
      "iwasawa main conjecture",
      "cm field",
      "artin motive",
      "algebraic hecke character",
      "absolute galois group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}