Abstract: In the 1950s and 1960s Tate proved some duality theorems in the Galois cohomology of finite modules and abelian varieties. As for most of Tate's work this has had a profound influence on mathematics with many applications and further developments. In this article, I discuss Tate's theorems and some of these developments.
The talk was my response to a request from the organizers:
We've chosen speakers to put aspects of Tate's work into perspective and point to the future so that the current and next generation can be inspired by them as much as our generations were. In particular, we'd be very grateful if you could speak on the theme of arithmetic duality.
The talk itself, is available on the web,
Video.
There a few misstatements in the video, but nothing serious (that I know of).
These are the slides for my talk, except that I've added a rough transcript of what I said while the slides were being displayed.