Non-Commutative LL-Functions for pp-Adic Representations over Totally Real Fields

  • Malte Witte

    Ruprecht-Karls-Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Non-Commutative $L$-Functions for $p$-Adic Representations over Totally Real Fields cover
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Abstract

We prove a unicity result for the non-commutative LL-functions for pp-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\rho of the absolute Galois group of a totally real field FF 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 LL-function for any such ρ\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.

Cite this article

Malte Witte, Non-Commutative LL-Functions for pp-Adic Representations over Totally Real Fields. Doc. Math. 24 (2019), pp. 1413–1511

DOI 10.4171/DM/708