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

作者：Lei, Antonio^*; Lim, Meng Fai

来源：BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 105(3): 419-430.

DOI：10.1017/S0004972721000976

• elliptic modular forms
• fine Selmer groups
• signed Selmer groups

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.

• 单位
  6; 1