Heights for line bundles on arithmetic surfaces
arXiv:alg-geom/9508003
Abstract
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on the Jacobian defined by the Theta divisor.
Mathematica Gottingensis, Heft 16, 1995, revised version, LaTeX2.09