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Heights for line bundles on arithmetic surfaces

Joerg Jahnel
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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.

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Joerg Jahnel. 1995-08-06. Heights for line bundles on arithmetic surfaces. https://arxiv.org/abs/alg-geom/9508003

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