[HG_A] Applications of Kolyvagin's conjecture to elliptic curves of arbitrary rank
ABSTRACT
In early 1990's, Kolyvagin formulated the conjecture on the non-triviality of Heegner point Kolyvagin systems motivated by understanding the arithmetic of elliptic curves of arbitrary rank. The conjecture itself is now proved for a large class of elliptic curves thanks to the work of Wei Zhang and its various generalizations. We discuss some interesting applications of Kolyvagin's conjecture as well as a different proof of Kolyvagin's conjecture for semi-stable elliptic curves with supersingular reduction.
