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Euler systems for modular forms over imaginary quadratic fields

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 April 2015

Antonio Lei ,
David Loeffler  and
Sarah Livia Zerbes
Antonio Lei
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Pavillon Alexandre-Vachon, 1045 avenue de la Médecine, Québec, QC, CanadaG1V 0A6 email antonio.lei@mat.ulaval.ca
David Loeffler
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK email d.a.loeffler@warwick.ac.uk
Sarah Livia Zerbes
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK email s.zerbes@ucl.ac.uk
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Abstract

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We construct an Euler system attached to a weight 2 modular form twisted by a Grössencharacter of an imaginary quadratic field $K$, and apply this to bounding Selmer groups.

MSC classification

Primary: 11F85: $p$-adic theory, local fields 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 9 , September 2015 , pp. 1585 - 1625
Copyright
© The Authors 2015 

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