Die Vermutung von Birch und Swinnerton-Dyer
نویسندگان
چکیده
منابع مشابه
The Birch-swinnerton-dyer Conjecture
We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
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A polynomial relation f(x, y) = 0 in two variables defines a curve C. If the coefficients of the polynomial are rational numbers then one can ask for solutions of the equation f(x, y) = 0 with x, y ∈ Q, in other words for rational points on the curve. If we consider a non-singular projective model C of the curve then over C it is classified by its genus. Mordell conjectured, and in 1983 Falting...
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This essay starts by first explaining, for elliptic curves defined over Q, the statement of the conjecture of Birch and Swinnerton-Dyer. Alongside, it contains a discussion of some results that have been proved in the direction of the conjecture, such as the theorem of Kolyvagin-Gross-Zagier and the weak parity theorem of Tim and Vladimir Dokchitser. The second, third and fourth part of the ess...
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In this talk I shall attempt to introduce some of the main features of the Birch and Swinnerton-Dyer conjecture, (BSD). The congruent number problem, deciding whether an integer D is the area of a right angle triangle with rational sides, is not easy. It turns out that the problem is equivalent to finding out if a certain elliptic curve has an infinite number of rational points. In 1983 Tunnell...
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The relationship between arithmetic objects (such as global fields, or varieties over global fields) and the analytic properties of their Lfunctions poses many deep and difficult questions. The theme of this paper is the Birch and Swinnerton Dyer conjecture, and certain refinements that were proposed by Mazur and Tate. We will formulate analogues of these conjectures over imaginary quadratic fi...
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ژورنال
عنوان ژورنال: Elemente der Mathematik
سال: 2002
ISSN: 0013-6018
DOI: 10.1007/pl00000565