Heights for line bundles on arithmetic varieties

Abstract

Let X be an arithmetic variety and L be an element of the Neron-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.