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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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