Hriljac, Paul Heights and Arakelov’s intersection theory. (English) Zbl 0593.14004 Am. J. Math. 107, 23-38 (1985). 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 Cited in 12 ReviewsCited in 33 Documents MSC: 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14H25 Arithmetic ground fields for curves 14G05 Rational points Keywords:Néron-Tate height; Jacobian varieties; Arakelov intersection theory on arithmetic surfaces; Hodge index theorem PDFBibTeX XMLCite \textit{P. Hriljac}, Am. J. Math. 107, 23--38 (1985; Zbl 0593.14004) Full Text: DOI