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

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.

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.

     author = {Tan, Ki-Seng},
     title = {Refined theorems of the Birch and Swinnerton-Dyer type},
     journal = {Annales de l'Institut Fourier},
     pages = {317--374},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {2},
     year = {1995},
     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, Tome 45 (1995) no. 2, pp. 317-374. doi : 10.5802/aif.1457.

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