Chan-Ho Kim

On the arithmetic of Tate-Shafarevich groups via Kolyvagin's conjecture

We investigate how Heegner points detect the finiteness of the $p$-primary part of Tate-Shafarevich groups of semi-stable elliptic curves over the rationals of \emph{arbitrary} rank with any good reduction prime $p \geq 5$ with irreducible mod $p$ representation and partially recover \c{C}iperiani--Wiles'theorem on sol...