Refined theorems of the Birch and Swinnerton-Dyer type

Ki-Seng Tan

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 2, page 317-374
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Tan, Ki-Seng. "Refined theorems of the Birch and Swinnerton-Dyer type." Annales de l'institut Fourier 45.2 (1995): 317-374. <http://eudml.org/doc/75121>.

@article{Tan1995,
abstract = {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},
journal = {Annales de l'institut Fourier},
keywords = {elliptic curve; -function; Birch-Swinnerton-Dyer conjecture; Mazur- Tate conjecture; height pairing; corrected discriminant},
language = {eng},
number = {2},
pages = {317-374},
publisher = {Association des Annales de l'Institut Fourier},
title = {Refined theorems of the Birch and Swinnerton-Dyer type},
url = {http://eudml.org/doc/75121},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Tan, Ki-Seng
TI - Refined theorems of the Birch and Swinnerton-Dyer type
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 2
SP - 317
EP - 374
AB - 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.
LA - eng
KW - elliptic curve; -function; Birch-Swinnerton-Dyer conjecture; Mazur- Tate conjecture; height pairing; corrected discriminant
UR - http://eudml.org/doc/75121
ER -

References

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