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Some local-global applications of Kummer theory

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Abstract.

 We consider some problems in number theory which turn out to depend on various aspects of Kummer theory; among them are (1) does the assertion ``b is in the subgroup generated by a'' obey a local-global principle for points of an algebraic group over a number field; (2) if two abelian varieties have the same n-division fields for n≥1, what relation is there between them?

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Authors and Affiliations

  1. Université Bordeaux I - A2X, 351, cours de la Libération, 33405 Talence Cedex, France. e-mail: emmanuel.kowalski@math.u-bordeaux.fr, , , , , , FR

    E. Kowalski

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  1. E. Kowalski
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Received: 24 September 2002 / Revised version: 15 November 2002 Published online: 20 March 2003

Mathematics Subject Classification (2000): Primary 11G99; Secondary 11R99, 11G10

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Kowalski, E. Some local-global applications of Kummer theory. manuscripta math. 111, 105–139 (2003). https://doi.org/10.1007/s00229-003-0356-6

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  • DOI: https://doi.org/10.1007/s00229-003-0356-6

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