Non-commutative L-functions for p-adic representations over totally real fields

• Verfasst von: Witte, Malte [VerfasserIn]
• Titel: Non-commutative L-functions for p-adic representations over totally real fields
• Verf.angabe: Malte Witte
• Jahr: 2019
• Umfang: 99 S.
• Fussnoten: Gesehen am 15.04.2020
• Titel Quelle: Enthalten in: Documenta mathematica
• Ort Quelle: Berlin : Deutsche Mathematiker-Vereinigung e.V., 1996
• Jahr Quelle: 2019
• Band/Heft Quelle: 24(2019), Seite 1413-1511
• ISSN Quelle: 1431-0643
• DOI: doi:10.25537/dm.2019v24.1413-1511
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: iwasawa theory
• Sach-SW: k-theory
• Sach-SW: main conjecture
• Sach-SW: Main Conjecture
• Sach-SW: non-commutative Iwasawa theory
• Sach-SW: totally real fields
• K10plus-PPN: 1694524191

Abstract

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.