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Jumps in Mordell-Weil Rank and Arithmetic Surjectivity

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Arithmetic of Higher-Dimensional Algebraic Varieties

Part of the book series: Progress in Mathematics ((PM,volume 226))

Abstract

We ask the question: If a pencil of curves of genus one defined over Q admits no section, can we find a number field L/Q and a member of that pencil defined over L having no L-rational points?

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Author information

Authors and Affiliations

  1. UC Berkeley, CA, 94720-3840, USA

    Tom Graber

  2. Harvard University, Cambridge, MA, 02138, USA

    Joseph Harris & Barry Mazur

  3. MIT, Cambridge, MA, 02139, USA

    Jason Starr

Authors
  1. Tom Graber
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  2. Joseph Harris
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  3. Barry Mazur
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  4. Jason Starr
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, Berkeley, CA, 94720, USA

    Bjorn Poonen

  2. Mathematisches Institut, Bunsenstr. 3-5, D-37073, Göttingen, Germany

    Yuri Tschinkel

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© 2004 Springer Science+Business Media New York

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Graber, T., Harris, J., Mazur, B., Starr, J. (2004). Jumps in Mordell-Weil Rank and Arithmetic Surjectivity. In: Poonen, B., Tschinkel, Y. (eds) Arithmetic of Higher-Dimensional Algebraic Varieties. Progress in Mathematics, vol 226. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8170-8_9

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  • DOI: https://doi.org/10.1007/978-0-8176-8170-8_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6471-2

  • Online ISBN: 978-0-8176-8170-8

  • eBook Packages: Springer Book Archive

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