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.
@article{AIF_1995__45_2_317_0, 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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.1457/} }
TY - JOUR AU - Tan, Ki-Seng TI - Refined theorems of the Birch and Swinnerton-Dyer type JO - Annales de l'Institut Fourier PY - 1995 SP - 317 EP - 374 VL - 45 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1457/ DO - 10.5802/aif.1457 LA - en ID - AIF_1995__45_2_317_0 ER -
%0 Journal Article %A Tan, Ki-Seng %T Refined theorems of the Birch and Swinnerton-Dyer type %J Annales de l'Institut Fourier %D 1995 %P 317-374 %V 45 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1457/ %R 10.5802/aif.1457 %G en %F AIF_1995__45_2_317_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1457/
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