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manuscripta mathematica

, Volume 96, Issue 4, pp 421–442 | Cite as

Heights for line bundles on arithmetic varieties

  • Jörg Jahnel
  • 26 Downloads

Abstract:

Let X be an arithmetic variety and L be an element of the Néron-Severi group of its generic fiber X K . Then there are only finitely many line bundles \(\) on X, generically belonging to L, such that the degrees of \(\) on the irreducible components of the special fibers of X and the height of \(\) are bounded. The concept of a height used here is recalled. Several elementary properties of this height are proven.

Mathematics Subject Classification (1991):14G40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jörg Jahnel
    • 1
  1. 1.Universität Göttingen, Mathematisches Institut, Bunsenstraße 3–5, D-37073 Göttingen, GermanyDE

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