Mathematics

Euler systems, in particular, the Heegner point Euler system have been integral to our approach to the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves. I will describe Kolyvagin's Euler system and how it can be used to approach the BSD conjecture. Then, I will describe work in progress on constructing such an Euler system associated to higher dimensional cycles in the function field setting.