Control Theorems for Fine Selmer Groups

We study the growth of p-primary fine Selmer group, R(E/F ′ ), an elliptic curve over intermediate sub-extension F a p-adic Lie extension, ℒ/F. estimate ℤ p -corank kernel and cokernel restriction map r ℒ/F :R(E/F )→R(E/ℒ) Gal(ℒ/F ) with finite extension contained in ℒ. show that groups these is related to structure group infinite level. On specializing certain (possibly non-commutative) extensions, we prove finiteness provide estimates on their orders.