Lang's Conjectures, Fibered Powers, and Uniformity.
Abramovich, Dan, Voloch, Jose Felipe (1996)
The New York Journal of Mathematics [electronic only]
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Abramovich, Dan, Voloch, Jose Felipe (1996)
The New York Journal of Mathematics [electronic only]
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W. J. Gordon (1979)
Compositio Mathematica
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Paul Vojta (1991)
Compositio Mathematica
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Ki-Seng Tan (1995)
Annales de l'institut Fourier
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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.
Serge Lang (1960)
Publications Mathématiques de l'IHÉS
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Guido Kings (2003)
Journal de théorie des nombres de Bordeaux
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This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.
W. Fulton, S. Kleiman, R. Piene, H. Tai (1985)
Bulletin de la Société Mathématique de France
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Michael Nakamaye (1999)
Journal de théorie des nombres de Bordeaux
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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.