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Explicit Serre weights for two-dimensional Galois representations

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  20 June 2017

Frank Calegari ,
Matthew Emerton ,
Toby Gee  and
Lambros Mavrides
Frank Calegari
Affiliation:
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA email fcale@math.uchicago.edu
Matthew Emerton
Affiliation:
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA email emerton@math.uchicago.edu
Toby Gee
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK email toby.gee@imperial.ac.uk
Lambros Mavrides
Affiliation:
Department of Mathematics, King’s College London, London WC2R 2LS, UK email lambros.mavrides@kcl.ac.uk
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Abstract

We prove the explicit version of the Buzzard–Diamond–Jarvis conjecture formulated by Dembele et al. (Serre weights and wild ramification in two-dimensional Galois representations, Preprint (2016), arXiv:1603.07708 [math.NT]). More precisely, we prove that it is equivalent to the original Buzzard–Diamond–Jarvis conjecture, which was proved for odd primes (under a mild Taylor–Wiles hypothesis) in earlier work of the third author and coauthors.

Keywords

Galois representationsHilbert modular forms

MSC classification

Primary: 11F80: Galois representations 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 9 , September 2017 , pp. 1893 - 1907
Copyright
© The Authors 2017 

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