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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 Çiperiani--Wile
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