Brylinski, Jean-Luc Heights for local systems on curves. (English) Zbl 0702.14016 Duke Math. J. 59, No. 1, 1-26 (1989). From the author’s introduction: “In this article, we develop a theory for a “motivic” local system V on a dense open set \(X^*\) of a smooth, projective algebraic curve X over a global field k. Such a theory was suggested by P. Deligne, on the basis of the work of B. H. Gross and D. B. Zagier [Invent. Math. 84, 225-320 (1986; Zbl 0608.14019)]... We explain, in an appendix, the relation of this theory to the higher-dimensional heights of A. Beilinson [Current trends in arithmetical algebraic geometry, Proc. Summer Res. Conf., Arcata/Calif. 1985, Contemp. Math. 67, 1-24 (1987; Zbl 0624.14005)]]. Reviewer: N.Manolache Cited in 1 ReviewCited in 5 Documents MSC: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights 14A20 Generalizations (algebraic spaces, stacks) 14G25 Global ground fields in algebraic geometry 14H45 Special algebraic curves and curves of low genus Keywords:motivic local system on a curve; heights Citations:Zbl 0608.14019; Zbl 0624.14005 PDFBibTeX XMLCite \textit{J.-L. Brylinski}, Duke Math. J. 59, No. 1, 1--26 (1989; Zbl 0702.14016) Full Text: DOI References: [1] A. Beilinson, Higher regulators and values of \(L\)-functions , J. Soviet Math. 30 (1985), 2036-2070. · Zbl 0588.14013 [2] A. Beuilinson, Height pairing between algebraic cycles , Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), Contemp. Math., vol. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 1-24. · Zbl 0624.14005 [3] A. Beilinson, J. Bernstein, and P. 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