Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)
نویسندگان
چکیده
منابع مشابه
Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture
In the first part of the talk we describe an algorithm which computes a relative algebraic K-group as an abstract abelian group. We also show how this representation can be used to do computations in these groups. This is joint work with Steve Wilson. Our motivation for this project originates from the study of the Equivariant Tamagawa Number Conjecture which is formulated as an equality of an ...
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We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
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 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
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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02572-5