6
votes
2answers
353 views

How did height in algeb. number theory/elliptic curves started?

Maybe this is obvious but it isn't to me yet. What is the history of heights used in say points of the project plane over a number field or of elliptic curve over a number field? I would guess people ...
11
votes
2answers
996 views

The parity conjecture

The parity conjecture for elliptic curves predicts that the rank of an elliptic curve defined over the rationals has the same parity as the p-Selmer rank for a prime number p. Could anyone familiar ...
9
votes
1answer
526 views

Historical question about modularity of CM curves

I'm looking for the answer of who first proved modularity of CM curves? That is if $E$ is an elliptic curve over $\mathbb{Q}$ which has complex multiplication then there's a non-constant morphism ...
14
votes
6answers
2k views

A non-technical account of the Birch—Swinnerton-Dyer Conjecture

I was wondering whether anyone knows of any good non-technical or even popular expositions of the Birch—Swinnerton-Dyer conjecture, for someone with minimal background in elliptic curves. I was ...