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

摘要

Let f be an elliptic modular form and p an odd prime that is coprime to the level of f We study the link between divisors of the characteristic ideal of the p-primary fine Selmer group of f over the cyclotomic Z(p) extension of Q and the greatest common divisor of signed Selmer groups attached to f defined 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 at p to the context of modular forms.

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