Document Zbl 0444.14015

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

Invent. Math. 58, 65-76 (1980).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0444.14015

MSC:

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

Keywords:

height pairings; Tamagawa numbers; Birch and Swinnerton-Dyer conjecture; Neron-Tate height; L-series of abelian variety; Tamagawa number; Shavarevic-Tate group; Picard group

Citations:

Zbl 0197.471; Zbl 0199.556; Zbl 0138.421; Zbl 0147.025; Zbl 0223.20050

Cite Review PDF

Full Text: DOI EuDML

References:

[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 · doi:10.2307/1970644
[4]	Ono, T.: Arithmetic of algebraic tori. Ann. of Math.,74, 101-139 (1961) · Zbl 0119.27801 · doi:10.2307/1970307
[5]	Ono, T.: On the Tamagawa number of algebraic tori. Ann. of Math.,78, 47-73 (1963) · Zbl 0122.39101 · doi:10.2307/1970502
[6]	Sansuc, Thèse, Paris (1978)
[7]	Tate, J.: The arithmetic of elliptic curves. Invent. Math.23, 179-206 (1974) · Zbl 0296.14018 · doi:10.1007/BF01389745
[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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.