Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer

W. J. Gordon

Compositio Mathematica (1979)

  • Volume: 38, Issue: 2, page 163-199
  • ISSN: 0010-437X

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Gordon, W. J.. "Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer." Compositio Mathematica 38.2 (1979): 163-199. <http://eudml.org/doc/89400>.

@article{Gordon1979,
author = {Gordon, W. J.},
journal = {Compositio Mathematica},
keywords = {Artin-Tate conjecture; Birch-Swinnerton-Dyer conjecture},
language = {eng},
number = {2},
pages = {163-199},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer},
url = {http://eudml.org/doc/89400},
volume = {38},
year = {1979},
}

TY - JOUR
AU - Gordon, W. J.
TI - Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 38
IS - 2
SP - 163
EP - 199
LA - eng
KW - Artin-Tate conjecture; Birch-Swinnerton-Dyer conjecture
UR - http://eudml.org/doc/89400
ER -

References

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  1. [1] M. Artin: Grothendieck topologies, notes on a seminar. Harvard University Press, Cambridge, Mass. (1962). Zbl0208.48701
  2. [2] M. Artin: Supersingular K3 surfaces, Ann. Sci. E.N.S., 4e série, 7 (1974) 4. Zbl0322.14014MR371899
  3. [3] M. Artin and H.P.F. Swinnerton-Dyer: The Shafarevich-Tate conjecture for pencils of elliptic curves on K3 surfaces, Inventiones Math., 20 (1973) 249-266. Zbl0289.14003MR417182
  4. [4] M. Artin and G. Winters: Degenerate fibers and stable reduction of curves, Topology10 (1974) 373-383. Zbl0196.24403MR476756
  5. [5] P. Deligne: La conjecture de Weil I, IHES Publ. Math., 43 (1974) 273-307. Zbl0287.14001MR340258
  6. [6] P. Deligne and D. Mumford: The irreducibility of the space of curves of a given genus, IHES Publ. Math., 36 (1969) 75-110. Zbl0181.48803MR262240
  7. [7] Éléments de géométrie algébrique, IHES Publ. Math., 4, 7, 11,... Zbl0203.23301
  8. [8] A. Grothendieck: Formule de Lefschetz et rationalite des fonctions L, Sém. Bourbaki279 (1964). Zbl0199.24802
  9. [9] A. Grothendieck: Le groupe de Brauer II, III. Dix exposés sur la cohomologie des schémas. North-Holland, Amsterdam (1968). 
  10. [10] A. Grothendieck: Les schémas de Picard, Sém. Bourbaki232 (1962). Zbl0238.14014
  11. [11] S. Lang: Abelian varieties. Interscience, New York (1959). Zbl0098.13201MR106225
  12. [12] S. Lang: Diophantine geometry. Interscience, New York (1962). Zbl0115.38701MR142550
  13. [13] S. Lang: Les formes bilinéaires de Néron et Tate, Sém. Bourbaki274 (1964). Zbl0138.42101MR176984
  14. [ 14] J. Lipman: Rational singularities... , IHES Publ. Math., 36 (1969) 195-280. Zbl0181.48903MR276239
  15. [15] J.S. Milne: The arithmetic of abelian varieties, Inventiones Math., 17 (1972) 177-190. Zbl0249.14012MR330174
  16. [16] J.S. Milne: On a conjecture of Artin and Tate, Annals of Math., 102 (1975) 517-533. Zbl0343.14005MR414558
  17. [17] J.S. Milne: The Brauer group of a rational surface, Inventiones Math., 11 (1970) 304-307. Zbl0205.25101MR285538
  18. [18] J.S. Milne: The Tate-Šafarevič group of a constant abelian variety, Inventiones Math., 6 (1968) 91-105. Zbl0159.22402MR244264
  19. [19] D. Mumford: Lectures on curves on an algebraic surface. Princeton University Press, Princeton (1966). Zbl0187.42701MR209285
  20. [20] A. Néron: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, IHES Publ. Math., 21 (1964). Zbl0132.41403MR179172
  21. [21] A. Néron: Problèmes arithmétiques et géométriques rattachés a la notion de rang d'une courbe algébrique dans un corps, Bull. Soc. Math. France, 80 (1952) 101-166. Zbl0049.30803MR56951
  22. [22] M. Raynaud: Spécialization du foncteur de Picard, IHES Publ. Math., 38 (1970) 27-76. Zbl0207.51602
  23. [23] SGA 4-Cohomologie étale des schémas. Lecture Notes in Mathematics269, 270, 305. Springer, Berlin etc. (1973). 
  24. [24] SGA 5-Cohomologie l-adic et fonctions L. Lecture Notes in Mathematics589. Springer, Berlin etc. (1977). Zbl0345.00011
  25. [25] J.T. Tate: On the conjecture of Birch and Swinnerton-Dyer and a geometric analogue, Sém. Bourbaki352 (1%8). Zbl0199.55604
  26. [26] J.T. Tate: "Algorithm for determining the type of a singular fiber in an elliptic curve." Modular functions of one variable IV. Lecture Notes in Mathematics476. Springer, Berlin etc. (1975). 
  27. [27] A. Weil: Adeles and algebraic groups. Institute for Advanced Study, Princeton (1961). Zbl0118.15801

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