Non-commutative L-functions for p-adic representations over totally real fields - Witte, Malte (Documenta mathematica, 2019)
We prove a unicity result for the Non-Commutative L-Functions for p-Adic Representations over Totally Real Fields-functions appearing in the non-commutative Iwasawa main conjecture over totally real fields. We then consider continuous representations rho 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 rho 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.
Gesehen am 15.04.2020