On the conjectures of Birch and Swinnerton-Dyer and a geometric analog

John Tate

Séminaire Bourbaki (1964-1966)

  • Volume: 9, page 415-440
  • ISSN: 0303-1179

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Tate, 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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  1. [1] M. Artin and A. Grothendieck - Cohomologie étale, Séminaire I.H.E.S., 1963-64, mimeographed. 
  2. [2] B.J. Birch - Conjectures on elliptic curves, Amer. Math. Soc., Proc. of Symposia in Pure Math., 8 : Theory of Numbers, Pasadena1963. 
  3. [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. [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. [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. [6] J.W.S. Cassels-Arithmetic on an elliptic curve, Proc. Int. Congress Math., Stockholm, 1962, 234-246. Zbl0118.27701MR175891
  7. [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. [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. [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. [10] A. Grothendieck - Fonctions L et cohomologie l-adique, Séminaire I.H.E.S., 1965, (in preparation). 
  11. [11] M. Kneser - Seminar talk at the Brighton Conference on Algebraic Number Theory, Sept. 1965, to appear in the Proceedings, Academic Press. 
  12. [12] S. Lang - Les formes bilinéaires de Néron et Tate, Séminaire Bourbaki, n°274 Mai 1964. Zbl0138.42101MR176984
  13. [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. [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. [15] A. Néron - Quasi-fonctions et hauteurs sur les variétés abéliennes, Annals of Math.82 (1965), 249-331. Zbl0163.15205MR179173
  16. [16] J.-P. Serre - Cohomologie Galoisienne, third edition, Lecture Notes in Mathematics, n° 5, Springer, 1965. Zbl0136.02801MR201444
  17. [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. [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. [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
  20. [20] J. Tate - Duality theorems in Galois cohomology over number fields, Proc. Int. Cong. Math., Stockholm (1962), 288-295. Zbl0126.07002MR175892
  21. [21] A. Weil - Jacobi sums as "Grössencharaktere". Trans. Amer. Math. Soc.73 (1952), 487-495. Zbl0048.27001MR51263
  22. [22] A. Weil - Adèles and algebraic groups, Mimeo notes taken by M. Demazure and T. Ono, I.A.S., Princeton, 1961. MR670072

Citations in EuDML Documents

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  1. Ian Morrison, Ulf Persson, Numerical sections on elliptic surfaces
  2. Gérard Ligozat, Fonction L des courbes modulaires
  3. Ki-Seng Tan, Refined theorems of the Birch and Swinnerton-Dyer type
  4. C. Soulé, The rank of étale cohomology of varieties over p -adic or number fields
  5. Peter Schneider, On the values of the zeta function of a variety over a finite field
  6. M. Artin, Supersingular K 3 surfaces
  7. Joseph Oesterlé, Empilements de sphères
  8. Dorian Goldfeld, Lucien Szpiro, Bounds for the order of the Tate-Shafarevich group
  9. Amílcar Pacheco, Sur le rang des variétés abéliennes sur un corps de fonctions
  10. Bernadette Perrin-Riou, Fonctions L p -adiques d’une courbe elliptique et points rationnels

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