On the μ-invariant of fine Selmer groups

On Fine Selmer Groups and Signed Selmer Groups of Elliptic Modular Forms

“…From [7, Conjecture A], [11, Conjecture A] and [1, Conjecture 1.2], the -invariants of and are predicted always to vanish. Corollary 4.6 gives an alternative formulation of these conjectures in terms of signed Selmer groups.…”

On fine Selmer groups and signed Selmer groups of elliptic modular forms

“…for ‚ P t7, 5u. 1 In loc. cit., it is assumed that f is non-ordinary at p, meaning that appf q is a non-unit in O.…”

“…We write M ι for the Λ-module which is M as an O-module equipped with a Γ-action given by γ ¨ι m " γ ´1m. Finally, if F P Λ " O X , we write F ι for the power series F p 1 1`X ´1q. For g " f or f and j P Z, let Sel 0 pA g pjq{Q cyc q denote the fine Selmer group of A g pjq over Q cyc (whose definition will be reviewed in §2.1).…”

“…See also [11,16,17,18,19] for some recent results on the topic. In the context of modular forms, the fine Selmer groups have been studied in [1,7,8,6].…”

Anticyclotomic $\largeμ$-invariants of residually reducible Galois Representations

“…The analysis of the fine Selmer groups is an essential part of K. Kato's seminal work on the Iwasawa Main Conjecture for elliptic curves and modular forms (see [19]). In recent years, their study has gained considerable momentum (see for instance [5,35,34,18,1]). J. Coates and R. Sujatha conjectured that the the fine Selmer group of E over F cyc is Λ-cotorsion with associated µ-invariant, µ fine (E/F cyc ), equal to zero [5,Conjecture A].…”