Refined theorems of the Birch and Swinnerton-Dyer type
Annales de l'Institut Fourier, Volume 45 (1995) no. 2, p. 317-374

In this paper, we generalize the context of the Mazur-Tate conjecture and sharpen, in a certain way, the statement of the conjecture. Our main result will be to establish the truth of a part of these new sharpened conjectures, provided that one assume the truth of the classical Birch and Swinnerton-Dyer conjectures. This is particularly striking in the function field case, where these results can be viewed as being a refinement of the earlier work of Tate and Milne.

Dans cet article nous généralisons le contexte de la conjecture de Mazur-Tate et dans une certaine mesure en donnons un énoncé plus fin. Nous prouvons ces nouvelles conjectures en supposant vraies les conjectures classiques de Birch et Swinnerton-Dyer. Ceci est remarquable dans le cas du corps des fonctions où ces résultats constituent une amélioration de travaux antérieurs de Tate et Milne.

     author = {Tan, Ki-Seng},
     title = {Refined theorems of the Birch and Swinnerton-Dyer type},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {2},
     year = {1995},
     pages = {317-374},
     doi = {10.5802/aif.1457},
     zbl = {0821.11036},
     mrnumber = {96j:11089},
     language = {en},
     url = {}
Tan, Ki-Seng. Refined theorems of the Birch and Swinnerton-Dyer type. Annales de l'Institut Fourier, Volume 45 (1995) no. 2, pp. 317-374. doi : 10.5802/aif.1457.

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