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Serre’s Conjecture for mod 7 Galois Representations

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Modular Curves and Abelian Varieties

Part of the book series: Progress in Mathematics ((PM,volume 224))

Abstract

We give an account of Serre’s conjecture for Galois representations with values in GL2(IF7). For this, we construct elliptic curves over totally real soluble extensions with given mod 7 representation, and use base change results to obtain modularity over ℚ.

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Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, UK

    Jayanta Manoharmayum

Authors
  1. Jayanta Manoharmayum
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    John E. Cremona

  2. Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Pau Gargallo, 5, 08028, Barcelona, Spain

    Joan-Carles Lario  & Jordi Quer  & 

  3. Department of Mathematics, University of California, M/C 3840, Berkeley, CA, 94720-3840, USA

    Kenneth A. Ribet

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© 2004 Springer Basel AG

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Manoharmayum, J. (2004). Serre’s Conjecture for mod 7 Galois Representations. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_10

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  • DOI: https://doi.org/10.1007/978-3-0348-7919-4_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9621-4

  • Online ISBN: 978-3-0348-7919-4

  • eBook Packages: Springer Book Archive

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