On the conjectures of Birch and Swinnerton-Dyer and a geometric analog
Séminaire Bourbaki (1964-1966)
- Volume: 9, page 415-440
- ISSN: 0303-1179
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topTate, John. "On the conjectures of Birch and Swinnerton-Dyer and a geometric analog." Séminaire Bourbaki 9 (1964-1966): 415-440. <http://eudml.org/doc/109707>.
@article{Tate1964-1966,
author = {Tate, John},
journal = {Séminaire Bourbaki},
keywords = {algebraic geometry},
language = {eng},
pages = {415-440},
publisher = {Société Mathématique de France},
title = {On the conjectures of Birch and Swinnerton-Dyer and a geometric analog},
url = {http://eudml.org/doc/109707},
volume = {9},
year = {1964-1966},
}
TY - JOUR
AU - Tate, John
TI - On the conjectures of Birch and Swinnerton-Dyer and a geometric analog
JO - Séminaire Bourbaki
PY - 1964-1966
PB - Société Mathématique de France
VL - 9
SP - 415
EP - 440
LA - eng
KW - algebraic geometry
UR - http://eudml.org/doc/109707
ER -
References
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- [2] B.J. Birch - Conjectures on elliptic curves, Amer. Math. Soc., Proc. of Symposia in Pure Math., 8 : Theory of Numbers, Pasadena1963.
- [3] B.J. Birch and H.P.F. Swinnerton-Dyer - Notes on elliptic curves. I, Journ. reine u. angewandte Math.212 (1963), 7-25. Zbl0118.27601MR146143
- [4] B.J. Birch and H.P.F. Swinnerton-Dyer - Notes on elliptic curves. II, Journ. reine u. angewandte Math.218 (1965), 79-108. Zbl0147.02506MR179168
- [5] J.W.S. Cassels - Arithmetic on curves of genus 1. I, II, III, IV, V, VI, VII, VIII,..., in particular, IV, Proof of the Hauptvermutung, Journ. reine u. angewandte Math.211 (1962) 95-112, and VIII, On Conjectures of Birch and Swinnerton-Dyer, Journ. reine u. angewandte Math.217 (1965), 180-199. Zbl0241.14017
- [6] J.W.S. Cassels-Arithmetic on an elliptic curve, Proc. Int. Congress Math., Stockholm, 1962, 234-246. Zbl0118.27701MR175891
- [7] J.W.S. Cassels-Arithmetic on abelian varieties, especially of dimension 1, Amer. Math. Soc., Lecture Notes of the Woods Hole Summer Institute on Algebraic Geometry, July 1964.
- [8] A. Grothendieck - Le groupe de Brauer I, Algèbres d'Azumaya et interprétations diverses, Séminaire Bourbaki, Mai 1965, n°290, 21 p., et II, Théorie cohomologique, Séminaire Bourbaki, Nov. 1965, n°297, 21 p. Zbl0193.21503
- [9] A. Grothendieck - Le groupe de Brauer III, Exemples et compléments, to appear in mimeo notes at the I.H.E.S. Zbl0198.25901MR244271
- [10] A. Grothendieck - Fonctions L et cohomologie l-adique, Séminaire I.H.E.S., 1965, (in preparation).
- [11] M. Kneser - Seminar talk at the Brighton Conference on Algebraic Number Theory, Sept. 1965, to appear in the Proceedings, Academic Press.
- [12] S. Lang - Les formes bilinéaires de Néron et Tate, Séminaire Bourbaki, n°274 Mai 1964. Zbl0138.42101MR176984
- [13] J.I. Manin - Tate height of points on abelian varieties, variants and applications, Isv. Akad. Nauk. S.S.S.R., Math. Series, 28, 6 (1964), 1363-1390. Zbl0192.26801MR173676
- [14] A. Néron - Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Inst. Hautes Etudes Scientifiques, n°21, 1964. Zbl0132.41403MR179172
- [15] A. Néron - Quasi-fonctions et hauteurs sur les variétés abéliennes, Annals of Math.82 (1965), 249-331. Zbl0163.15205MR179173
- [16] J.-P. Serre - Cohomologie Galoisienne, third edition, Lecture Notes in Mathematics, n° 5, Springer, 1965. Zbl0136.02801MR201444
- [17] J.-P. Serre - Zeta and L-functions, to appear in the proceedings of the Purdue Conference on Arithmetical Algebraic Geometry, to be published by Harper and Row. (This has appeared in the A.M.S. Mimeo proceedings of the Woods Hole Summer Institute on Algebraic Geometry, July, 1964, and also in Russian translation in the most recent issue of Uspekhi). Zbl0171.19602MR194396
- [18] H.P.F. Swinnerton-Dyer - Seminar talk at the Brighton conference on algebraic number theory, to appear in the proceedings with Academic Press. MR314733
- [19] J. Tate-Algebraic cycles and poles of zeta functions, to appear in the proceedings of the Purdue Conference on Arithmetical Algebraic Geometry, to be published by Harper and Row. (This is a very slight modification of the talk on Algebraic cohomology classes which has appeared in the A.M.S. Mimeo proceedings of the Woods Hole Summer Institute on Algebraic Geometry, July, 1964, and also in Russian translation in the most recent issue of Uspekhi.) Zbl0213.22804MR225778
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Citations in EuDML Documents
top- Ian Morrison, Ulf Persson, Numerical sections on elliptic surfaces
- Gérard Ligozat, Fonction L des courbes modulaires
- Ki-Seng Tan, Refined theorems of the Birch and Swinnerton-Dyer type
- C. Soulé, The rank of étale cohomology of varieties over -adic or number fields
- Peter Schneider, On the values of the zeta function of a variety over a finite field
- M. Artin, Supersingular surfaces
- Joseph Oesterlé, Empilements de sphères
- Dorian Goldfeld, Lucien Szpiro, Bounds for the order of the Tate-Shafarevich group
- Bernadette Perrin-Riou, Fonctions -adiques d’une courbe elliptique et points rationnels
- Amílcar Pacheco, Sur le rang des variétés abéliennes sur un corps de fonctions
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