# The Birch and Swinnerton-Dyer conjecture and a geometric analog(ue)

## by John Tate

## What it is about

The first part of the paper described the BSD conjecture in general functorial
terms, and is the first place where it was stated for abelian varieties. This
more general formulation is due to Tate, but he shrugs off credit for it. Tate
then discusses why if the conjecture is true for an abelian variety A, it is
automatically true for any abelian variety isogenous to A, a result that inspired
his global duality theorem. Next he gives an analogue of the Shafarevich-Tate
group in a geometric context and relates it to the Brauer group of a curve.

## Electronic Version

Here is a 12MB
scan of the paper in PDF format.