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Heights and Arakelov’s intersection theory. (English) Zbl 0593.14004

In this article the author relates the Néron-Tate height on Jacobian varieties to Arakelov intersection theory on arithmetic surfaces. The Arakelov intersection pairing is shown to be a Néron pairing. The connection between intersection multiplicities and Néron functions is developed. Finally, an analog of the Hodge index theorem for arithmetic surfaces is proved using the above results.
Reviewer: L.D.Olson

MSC:

14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14H25 Arithmetic ground fields for curves
14G05 Rational points
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