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Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia
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 $\mathbb{Z}_p$-extension of $\mathbb{Q}$ 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.

Keywords:cyclotomic extension, Shafarevich-Tate group, Bloch-Kato Selmer group, modular form, non-ordinary prime, p-adic Hodge theory
Categories:11R18, 11F11, 11R23, 11F85

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