ON FINE SELMER GROUPS AND SIGNED SELMER GROUPS OF ELLIPTIC MODULAR FORMS

Abstract

AbstractLetfbe an elliptic modular form andpan odd prime that is coprime to the level off. We study the link between divisors of the characteristic ideal of thep-primary fine Selmer group offover the cyclotomic$\mathbb {Z}_p$extension of$\mathbb {Q}$and the greatest common divisor of signed Selmer groups attached tofdefined using the theory of Wach modules. One of the key ingredients of our proof is a generalisation of a result of Wingberg on the structure of fine Selmer groups of abelian varieties with supersingular reduction atpto the context of modular forms.