A note on height pairings, Tamagawa numbers, and the Birch and Swinnerton-Dyer conjecture. (English) Zbl 0444.14015


14G05 Rational points
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H25 Arithmetic ground fields for curves
14K15 Arithmetic ground fields for abelian varieties
14K05 Algebraic theory of abelian varieties
Full Text: DOI EuDML


[1] Lang, S.: Les formes bilinéaires de Néron et Tate. Sem. Bourbaki, no 274, 1964 · Zbl 0138.42101
[2] Manin, Ju., Zarkin, Y.G.: Heights on families of abelian varieties. Mat. Sbornik89, 171-181 (1972)
[3] Néron, A.: Quasi-fonctions et hauteurs sur les variétés abéliennes. Annals of Math.82, 249-331 (1965) · Zbl 0163.15205
[4] Ono, T.: Arithmetic of algebraic tori. Ann. of Math.,74, 101-139 (1961) · Zbl 0119.27801
[5] Ono, T.: On the Tamagawa number of algebraic tori. Ann. of Math.,78, 47-73 (1963) · Zbl 0122.39101
[6] Sansuc, Thèse, Paris (1978)
[7] Tate, J.: The arithmetic of elliptic curves. Invent. Math.23, 179-206 (1974) · Zbl 0296.14018
[8] Tate, J.: On the conjecture of Birch and Swimmerton-Dyer and a geometric analog. Sem. Bourbaki No.306, Feb. 1966 · Zbl 0199.55604
[9] Tate, J.: Letter to Serre, June 21, 1968
[10] Weil, A.: Adèles and algebraic groups. Institute for Advanced Study, Princeton, 1961 · Zbl 0109.02101
[11] Mazur, B., Messing, W.: Universal extensions and one-dimensional crystalline cohomology. Lecture Notes in Math. No.370, Berlin-Heidelberg-New York: Springer 1974 · Zbl 0301.14016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.