Abstract
Let E be an elliptic curve with either good ordinary or split multiplicative reduction at each prime above p. Coates et al has developed an algebraic K-theoretical approach of attaching characteristic elements to the Selmer group of E over a non-commutative p-adic Lie extension. In this talk, we explain how these characteristic elements "captures" the Selmer ranks of the intermediate subextensions of the said p-adic Lie extension. If time permits, we will also mention some on-going investigation of the situation (and difficulties faced) when E has good supersingular reduction at p.
