1. $p$-adic $L$-function and Iwasawa Main Conjecture for an Artin motive over a CM field
- Author
-
Hara, Takashi and Ochiai, Tadashi
- Subjects
Mathematics - Number Theory ,11R23 (Primary), 11F41, 11F67 (Secondaries) - 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., Comment: 38 pages, unintended outputs (the diagram (4.10) and the diagram at the sixth line from the bottom of page 28) are fixed
- Published
- 2024