The Birch and Swinnerton-Dyer Conjecture
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چکیده
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 found a simple condition for this to be truedependent upon the truth of the ’weak’ BSD. The Birch and Swinnerton-Dyer conjecture was formulated in the 1960s based on computational evidence and is a set of interlinked conjectures about the L-function of an abelian variety defined over a global field. A lot of work has been done and some special cases have been established, but the conjecture is still unproved in general.
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