A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field
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.
متن کاملThe conjecture of Birch and Swinnerton-Dyer
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...
متن کاملThe Birch and Swinnerton-Dyer Conjecture
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...
متن کاملThe Birch and Swinnerton-Dyer Conjecture
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...
متن کاملThe Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields
1 Algebraic Groups 7 1.1 Group Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Restriction of Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Algebraic Groups over a Nonalgebraically Closed Field K . . . . . . . . . . . 13 1.4 Structure of Algebraic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Topologizing G(R...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2004
ISSN: 0022-040X
DOI: 10.4310/jdg/1102536710