The Birch and Swinnerton-Dyer Conjecture

by

A. Wiles

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

,i n 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.

 

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