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Arithmetic Part of Faltings’s Proof

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1566)

Abstract

In this chapter we will follow §5 of [22] quite closely. We start in the following situation:

k is a number field, A k is an abelian variety over k, X k A k is a subvariety such that \( X_{\bar k} \) does not contain any translate of a positive dimensional abelian subvariety of \( A_{\bar k} \), m is a sufficiently large integer as in Chapter IX, Lemma 1

Let R be the ring of integers in k. Since we want to apply Faltings’s version of Siegel’s Lemma (see Ch. X, Lemma 4) we need lattices in things like г(X m k , line bundle). We obtain such lattices as:

г(proper model of X m k over R, extension of line bundle).

Keywords

  • Line Bundle
  • Abelian Variety
  • Finite Type
  • Global Section
  • Pole Order

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.

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© 1993 Springer-Verlag Berlin Heidelberg

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Edixhoven, B. (1993). Arithmetic Part of Faltings’s Proof. In: Edixhoven, B., Evertse, JH. (eds) Diophantine Approximation and Abelian Varieties. Lecture Notes in Mathematics, vol 1566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48208-6_11

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  • DOI: https://doi.org/10.1007/978-3-540-48208-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57528-3

  • Online ISBN: 978-3-540-48208-6

  • eBook Packages: Springer Book Archive