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Proof of Manin’s theorem by reduction to positive characteristic

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1696)

Abstract

We explain in this note how to deduce a characteristic 0 Mordell-Lang statement for function fields from the positive characteristic version. See the contributions of Bouscaren and Hindry to this volume for the general statement of Mordell-Lang. (See also [Lan 91] for the history and further references.) While we see no obstacle to proving the general statement by the same method, we will restrict the statement to abelian varieties and rational points.

Keywords

  • Function Field
  • Abelian Variety
  • Finite Extension
  • Torsion Point
  • Morley Rank

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Author partially supported by a grant from the NSF.

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© 1998 Springer-Verlag Berlin Heidelberg

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Hrushovski, E. (1998). Proof of Manin’s theorem by reduction to positive characteristic. In: Bouscaren, E. (eds) Model Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68521-0_11

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  • DOI: https://doi.org/10.1007/978-3-540-68521-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64863-5

  • Online ISBN: 978-3-540-68521-0

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