Geodesic
Non-Commutative $L$-Functions for $p$-Adic Representations over Totally Real Fields
Documenta mathematica, Tome 24 (2019), pp. 1413-1511
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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 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.
DOI : 10.4171/dm/708
Classification : 11R23, 11R42, 19F27
Mots-clés : main conjecture, non-commutative Iwasawa theory, totally real fields 
@article{10_4171_dm_708,
     author = {Malte Witte},
     title = {Non-Commutative $L${-Functions} for $p${-Adic} {Representations} over {Totally} {Real} {Fields}},
     journal = {Documenta mathematica},
     pages = {1413--1511},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/708},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/708/}
}
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Malte Witte. Non-Commutative $L$-Functions for $p$-Adic Representations over Totally Real Fields. Documenta mathematica, Tome 24 (2019), pp. 1413-1511. doi: 10.4171/dm/708

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