In mathematicsthe birch and swinnertondyer conjecture describes the set of rational solutions to equations defining an elliptic curve. Scribd is the worlds largest social reading and publishing site. Here, daniel delbourgo explains the birch and swinnertondyer conjecture. The conjecture was chosen as one of the seven millennium prize problems listed by the clay mathematics institute, which has. Il rango di eq e uguale allordine di annullamento di leq. Taking wedge products of these harmonic representatives corresponds to the cup product in cohomology, so the cup product is compatible with the hodge decomposition the assumption in the hodge conjecture that x be algebraic projective complex manifold cannot be weakened. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. Cualquier informacion por favor contactarme al inbox. In mathematics, the birch and swinnertondyer conjecture describes the set of rational solutions to equations defining an elliptic curve.
The birch and swinnertondyer conjecture clay mathematics institute. List of unsolved problems in mathematics free download as pdf file. In mathematics, the birch and swinnertondyer conjecture describes the set of rational. On the conjecture of birch and swinnertondyer for an elliptic curve. Nb that the reciprocal of the lfunction is from some points of view a more natural object of study. Report on the birch and swinnertondyer conjecture article pdf available in milan journal of mathematics 781. A diophantine equation is an algebraic equation in unknown variables x, y. The lefschetz theorem on 1,1 classes also implies that if all hodge classes are generated by the hodge classes of divisors, then the hodge conjecture is true arithmetic theory of elliptic curves. Q, in other words for rational points on the curve. On the conjectures of birch and swinnertondyer and a.
The number of independent basis points with infinite order is called the rank of the curve, and. Birch and swinnertondyer conjecture clay mathematics institute. Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to. Birch and swinnertondyer, has been verified in some special cases, notably for.