On the Asymptotic Growth ofBloch-Kato-Shafarevich-Tate Groups ofModular Forms Over CyclotomicExtensions

2016/09/29 by Antonio Lei, David Loeffler, Zerbes Sarah Livia · 5 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.4153/cjm-2016-034-x

Abstract

Abstract 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.

Cited by

• On the growth of Tate-Shafarevich groups of p-supersingular abelian varieties of \rm GL₂-type over ℤ_p-extensions of number fields
• Iwasawa theory of automorphic representations of GL_2n at non-ordinary primes
• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
• On the Iwasawa main conjectures for modular forms at non-ordinary primes
• Ranks of elliptic curves over Z_p²-extensions

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• Vanishing of the p-part of the Shafarevich-Tate group of a modular form and its consequences for Anticyclotomic Iwasawa Theory