Summary: The purpose of this paper is to propose a new construction of Néron pairings [see A. Néron, Ann. Math., II. Ser. 82, 249-331 (1965; Zbl 0163.15205)] based on an interpretation of local heights (Weil’s distributions) [A. Weil, Ann. Math., II. Ser. 53, 412-444 (1951; Zbl 0043.27002)] as logarithms of homogeneous functions on linear vector bundles (with deleted zero section), and consequent application of Tate’s trick. This approach allows to obtain easily group-theoretic interpretation of Néron pairings à la Yu. G. Zarkhin [Math. USSR, Izv. 6(1972), 491-503 (1973); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 36, 497-509 (1972; Zbl 0244.14009)]. Notice that the proposed interpretation of local height has already proved its usefulness during the check up of the coincidence of various definitions of the canonical height of an Abelian variety [see Yu. G. Zarkhin and A. N. Parshin in: Transl. II. Ser., Ann. Math. Soc. 143, 35-102 (1989; Zbl 0672.14012); translation from the (Russian) appendix to the Russian translation of S. Lang’s book: “Fundamentals of Diophantine geometry” (1986)]. This paper is closely related to the author’s article in Sémin. Théor. Nombres, Paris 1987-88, Prog. Math. 81, 317-341 (1990; Zbl 0707.14040)].
For the entire collection see [Zbl 0863.00012].