On fine Selmer groups and the greatest common divisor of signed and chromatic p-adic L-functions

Let E/\mathbb {Q} be an elliptic curve and p an odd prime where E has good supersingular reduction. Let F_1 denote the characteristic power series of the Pontryagin dual of the fine Selmer group of E over the cyclotomic \mathbb {Z}_p-extension of \mathbb {Q} and let F_2 denote the greatest common divisor of Pollack’s plus and minus p-adic L-functions or Sprung’s sharp and flat p-adic L-functions attached to E, depending on whether a_p(E)=0 or a_p(E)\ne 0. We study a link between the divisors of F_1 and F_2 in the Iwasawa algebra. This gives new insights into problems posed by Greenberg and Pollack–Kurihara on these elements.