On the Asymptotic Growth of Bloch-Kato-Shafarevich-Tate Groups of Modular Forms Over Cyclotomic Extensions

We study the asymptotic behaviour of the Bloch-Kato-Shafarevich-Tate group of a modular form f over the cyclotomic Z(p)-extension of Q under the assumption that f is non-ordinary at p. In particular, we give upper bounds of these groups in terms of Iwasawa invariants of Selmer groups defined using p-adic Hodge Theory. These bounds have the same form as the formulae of Kobayashi, Kurihara, and Sprung for supersingular elliptic curves.