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EULER SYSTEMS FOR HILBERT MODULAR SURFACES

Part of: Discontinuous groups and automorphic forms Algebraic number theory: global fields

Published online by Cambridge University Press:  15 November 2018

ANTONIO LEI Open the ORCID record for ANTONIO LEI [Opens in a new window] ,
DAVID LOEFFLER Open the ORCID record for DAVID LOEFFLER [Opens in a new window]  and
SARAH LIVIA ZERBES Open the ORCID record for SARAH LIVIA ZERBES [Opens in a new window]
ANTONIO LEI
Affiliation:
Département de mathématiques et de statistique, Pavillon Alexandre-Vachon, Université Laval, Québec, QC, Canada G1V 0A6; antonio.lei@mat.ulaval.ca
DAVID LOEFFLER
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK; d.a.loeffler@warwick.ac.uk
SARAH LIVIA ZERBES
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK; s.zerbes@ucl.ac.uk

Abstract

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We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, this Euler system is nontrivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.

MSC classification

Primary: 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F80: Galois representations 11R23: Iwasawa theory
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e23
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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