Under ordinary p and p>k+1 with standard residual assumptions, the strong Kolyvagin conjecture for even-weight newforms holds: derived Heegner-cycle cohomology classes are nonzero.
Zhang, Selmer groups and the indivisibility of Heegner points , Camb
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Kolyvagin's conjecture for modular forms
Under ordinary p and p>k+1 with standard residual assumptions, the strong Kolyvagin conjecture for even-weight newforms holds: derived Heegner-cycle cohomology classes are nonzero.