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On the Asymptotic Growth of Bloch–Kato–Shafarevich–Tate Groups of Modular Forms Over Cyclotomic Extensions
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- Journal:
- Canadian Journal of Mathematics / Volume 69 / Issue 4 / 01 August 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 826-850
- Print publication:
- 01 August 2017
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- Article
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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.
