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Displaying similar documents to “Lang’s conjecture in characteristic p : an explicit bound”

Refined theorems of the Birch and Swinnerton-Dyer type

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.

The Bloch-Kato conjecture on special values of L -functions. A survey of known results

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.

Diophantine approximation on algebraic varieties

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.