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- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
- ISSN
- 2522-0144
- eISSN
- 2197-9847
- DOI
- 10.1007/s40687-022-00360-0
- Publisher site
- See Article on Publisher Site
Abstract
Let Π\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Pi $$\end{document} be a cuspidal automorphic representation of GL2n(AQ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textrm{GL}}_{2n}({\mathbb {A}}_{\mathbb {Q}})$$\end{document}, and let p be an odd prime at which Π\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Pi $$\end{document} is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded p-adic L-functions interpolating complex L-values of Π\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Pi $$\end{document} in the non-ordinary case. Under certain assumptions, we construct two boundedp-adic L-functions for Π\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Pi $$\end{document}, thus extending an earlier work of Rockwood by relaxing the Pollack condition. Using Langlands local–global compatibility, we define signed Selmer groups over the p-adic cyclotomic extension of Q\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {Q}$$\end{document} attached to the p-adic Galois representation of Π\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Pi $$\end{document} and formulate Iwasawa main conjectures in the spirit of Kobayashi’s plus and minus main conjectures for p-supersingular elliptic curves.
Journal
Research in the Mathematical Sciences – Springer Journals
Published: Mar 1, 2023
Keywords: Automorphic representations; Non-ordinary primes; p-adic L-functions; Iwasawa main conjecture; Primary: 11R23; Secondary: 11F70; 11F80; 11F67