L-invariants of Artin motives

Dimitrov, Mladen; MAKSOUD, Alexandre

doi:10.1007/s40316-022-00201-0

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L-invariants of Artin motives

Dimitrov, Mladen; MAKSOUD, Alexandre

2022 • In Annales mathématiques du Québec

Peer reviewed

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https://hdl.handle.net/10993/51830

DOI
10.1007/s40316-022-00201-0

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Keywords :

L-invariants; p-adic L-functions; Galois representations; weight one modular forms

Abstract :

[en] We compute Benois L-invariants of weight 1 cuspforms and of their adjoint representations and show how this extends Gross’ p-adic regulator to Artin motives which are not critical in the sense of Deligne. Benois’ construction depends on the choice of a regular submodule which is well understood when the representation is p-regular, as it then amounts to the choice of a “motivic” p-refinement. The situation is dramatically different in the p-irregular case, where the regular submodules are parametrized by a flag variety and thus depend on continuous parameters. We are nevertheless able to show in some examples, how Hida theory and the geometry of the eigencurve can be used to detect a finite number of choices of arithmetic and “mixed-motivic” significance.

Disciplines :

Mathematics

Author, co-author :

Dimitrov, Mladen; University of Lille

MAKSOUD, Alexandre ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

yes

Language :

English

Title :

L-invariants of Artin motives

Publication date :

27 July 2022

Journal title :

Annales mathématiques du Québec

Peer reviewed :

Peer reviewed

FnR Project :

FNR12589973 - Galois Representations, Automorphic Forms And Their L-functions, 2018 (01/02/2019-31/08/2024) - Gabor Wiese

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since 01 August 2022

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