In [A2] and [A3], Arakelov introduces an intersection calculus for arithmetic surfaces, that is, for stable models of curves over a number field. In this paper we intend to show that his intersection product has a lot of useful properties. More precisely, we show that the following properties from the theory of algebraic surfaces have an analogue in our situation:
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Герд Фалтингс (1984) studied this question.
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