Geodesic
Non-Commutative $L$-Functions for $p$-Adic Representations over Totally Real Fields
Documenta mathematica, Tome 24 (2019), pp. 1413-1511.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11R23, 11R42, 19F27
Keywords: main conjecture, non-commutative Iwasawa theory, totally real fields 
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     author = {Witte, Malte},
     title = {Non-Commutative {\(L\)-Functions} for {\(p\)-Adic} {Representations} over {Totally} {Real} {Fields}},
     journal = {Documenta mathematica},
     pages = {1413--1511},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a27/}
}
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Witte, Malte. Non-Commutative \(L\)-Functions for \(p\)-Adic Representations over Totally Real Fields. Documenta mathematica, Tome 24 (2019), pp. 1413-1511. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a27/