Abstract
The purpose of this part is to give an introduction to intersection theory on arithmetic surfaces, a theory initiated by S.Yu Arakelov in [A1,2,3] and further developped by G. Faltings in [F]. The idea, propagated during the last years in particular by L. Szpiro, is roughly to replace or better to enrich algebro-geometric structures at the infinite primes involved by hermitian structures as for example hermitian line bundles, curvatures, volumes etc.
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