Year: 2017
Type: preprint
Abstract: We prove a unicity result for the $L$-functions appearing in the non-commutative Iwasawa main conjecture over totally real fields. We then consider continuous representations $ρ$ of the absolute Galois group of a totally real field $F$ on adic rings in the sense of Fukaya and Kato. Using our unicity result, we show that there exists a unique sensible definition of a non-commutative $L$-function for any such $ρ$ that factors through the Galois group of a possibly infinite totally real extension. We also consider the case of CM-extensions and discuss the relation with the equivariant main conjecture for realisations of abstract $1$-motives of Greither and Popescu.
Source: arXiv (Cornell University)
Author: Witte, Malte
Institution: Heidelberg University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4295888549