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- Publisher
- Springer Journals
- Copyright
- Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2022
- ISSN
- 2195-4755
- eISSN
- 2195-4763
- DOI
- 10.1007/s40316-022-00201-0
- Publisher site
- See Article on Publisher Site
Abstract
R\'esum\'eWe compute Benois L\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathscr {L}}$$\end{document}-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.
Journal
Annales mathématiques du Québec – Springer Journals
Published: Apr 1, 2023
Keywords: L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {L}}$$\end{document}-invariants; p-adic L-functions; Galois representations; Weight one modular forms; 11R23; 11F80; 11F33