THE PLUS/MINUS SELMER GROUPS FOR SUPERSINGULAR PRIMES

Suppose that an elliptic curve E over Q has good supersingular reduction at p. We prove that Kobayashi's plus/minus Selmer group of E over a Z(p)-extension has no proper Lambda-submodule of finite index under some suitable conditions, where Lambda is the Iwasawa algebra of the Galois group of the Z(p)-extension. This work is analogous to Greenberg's result in the ordinary reduction case.