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In this article we prove a refinement of a theorem of Longo and Vigni in theanticyclotomic Iwasawa theory for modular forms. More precisely we give adefinition for the ($\mathfrak{p}$-part of the) Shafarevich-Tate groups$\widetilde{\mathrm{sha}}_{\mathfrak{p}^\infty}(f/K)$ and$\widetilde{\mathrm{sha}}_{\mathfrak{p}^\infty}(f/K_\infty)$ of a modular form$f$ of weight $k >2$, over an imaginary quadratic field $K$ satisfying theHeegner hypothesis and over its anticyclotomic $\mathbb{Z}_p$-extension$K_\infty$ and we show that if the basic generalized Heegner cycle $z_{f, K}$is non-torsion and not divisible by $p$, then$\widetilde{\mathrm{sha}}_{\mathfrak{p}^\infty}(f/K) =\widetilde{\mathrm{sha}}_{\mathfrak{p}^\infty}(f/K_\infty) = 0$.

Vanishing of the p-part of the Shafarevich-Tate group of a modular form and its consequences for Anticyclotomic Iwasawa Theory