Geodesic
On the Asymptotic Growth ofBloch–Kato–Shafarevich–Tate Groups ofModular Forms Over CyclotomicExtensions
Canadian journal of mathematics, Tome 69 (2017) no. 4, pp. 826-850

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DOI

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.
DOI : 10.4153/CJM-2016-034-x
Mots-clés : 11R18, 11F11, 11R23, 11F85, cyclotomic extension, Shafarevich-Tate group, Bloch-Kato Selmer group, modular form, non-ordinary prime, p-adic Hodge theory 
Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia. On the Asymptotic Growth ofBloch–Kato–Shafarevich–Tate Groups ofModular Forms Over CyclotomicExtensions. Canadian journal of mathematics, Tome 69 (2017) no. 4, pp. 826-850. doi: 10.4153/CJM-2016-034-x
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     author = {Lei, Antonio and Loeffler, David and Zerbes, Sarah Livia},
     title = {On the {Asymptotic} {Growth} {ofBloch{\textendash}Kato{\textendash}Shafarevich{\textendash}Tate} {Groups} {ofModular} {Forms} {Over} {CyclotomicExtensions}},
     journal = {Canadian journal of mathematics},
     pages = {826--850},
     year = {2017},
     volume = {69},
     number = {4},
     doi = {10.4153/CJM-2016-034-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-034-x/}
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