On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions

Abstract

We study the asymptotic behaviour of the Bloch-Kato-Shafarevich-Tate group of a modular form f over the cyclotomic Zp-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.

To appear in Canad. J. Math

References in corpus (1)

• Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions

Cited by in corpus (12)

• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• On the Iwasawa main conjectures for modular forms at non-ordinary primes
• Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions
• Ranks of elliptic curves over Z_p^2-extensions
• Rank--two Euler systems for symmetric squares
• Arithmetic properties of signed Selmer groups at non-ordinary primes
• Iwasawa theory for Symmetric Square of non-$p$-ordinary eigenforms
• Functional Equation for p-adic Rankin-Selberg L-functions
• Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes
• On the structure of the Bloch--Kato Selmer groups of modular forms over anticyclotomic ${\mathbf{Z}}_p$-towers
• Iwasawa theory of automorphic representations of ${\mathrm{GL}}_{2n}$ at non-ordinary primes
• $p^r$-Selmer companion modular forms