On the corank of the fine Selmer group of an elliptic curve over a Zp-extension

Let p be an odd prime and F ∞ be a Z p -extension of a number field F . Given an elliptic curve E over F , we study the structure of the fine Selmer group over F ∞ . It is shown that under certain conditions, the fine Selmer group is a cofinitely generated module over Z p and furthermore, we obtain an upper bound for its corank (i.e. the λ -invariant), in terms of various local and global invariants.