Heights for line bundles on arithmetic varieties
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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.
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