Galois theory, elliptic curves, and root numbers
David E. Rohrlich (1996)
Compositio Mathematica
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Displaying similar documents to “Elliptic curves and local -factors”
Galois theory, elliptic curves, and root numbers
2-torsion of the Brauer group of an elliptic curve: Generators and relations.
Chernousov, V., Guletskiĭ, V. (2001)
Documenta Mathematica
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Variation of the root number in families of elliptic curves
David E. Rohrlich (1993)
Compositio Mathematica
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On octahedral extensions of and quadratic -curves
Julio Fernández (2003)
Journal de théorie des nombres de Bordeaux
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We give a necessary condition for a surjective representation Gal to arise from the -torsion of a -curve. We pay a special attention to the case of quadratic -curves.
Elliptic curves and class fields of real quadratic fields: Algorithms and evidence.
Darmon, Henri, Green, Peter (2002)
Experimental Mathematics
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The splitting of primes in division fields of elliptic curves.
Duke, W., Tóth, Á. (2002)
Experimental Mathematics
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Elliptic curves and special values of L-series.
Massimo Bertolini (1997)
Collectanea Mathematica
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From the Taniyama-Shimura conjecture to Fermat's last theorem
Kenneth A. Ribet (1990)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.