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Abelian Varieties over ℚ with Large Endomorphism Algebras and Their Simple Components over \( \overline Q\)

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Modular Curves and Abelian Varieties

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

Abstract

This dissertation expands upon the results of K. Ribet in [Ri 1] and [Ri 2] concerning abelian varieties “of GL2-type”. An abelian variety A/ℚ is said to be of GL2-type if its algebra of ℚ-endomorphisms ℚ ® Endℚ(A) is a number field E of degree equal to the dimension of A.

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Author information

Authors and Affiliations

  1. Annapolis, Maryland, USA

    Elisabeth E. Pyle

Authors
  1. Elisabeth E. Pyle
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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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Pyle, E.E. (2004). Abelian Varieties over ℚ with Large Endomorphism Algebras and Their Simple Components over \( \overline Q\) . 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_14

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  • DOI: https://doi.org/10.1007/978-3-0348-7919-4_14

  • 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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