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On the Asymptotic Growth ofBloch–Kato–Shafarevich–Tate Groups ofModular Forms Over CyclotomicExtensions
Published online by Cambridge University Press: 20 November 2018
Abstract
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
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- Research Article
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- Copyright © Canadian Mathematical Society 2017
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