On order of vanishing of characteristic elements

Abstract

AbstractLetpbe a fixed odd prime. LetEbe an elliptic curve defined over a number fieldFwith either good ordinary reduction or multiplicative reduction at each prime ofFabovep. We shall study the characteristic element of the Selmer group ofEover ap-adic Lie extension. In particular, we relate the order of vanishing of these characteristic elements evaluated at Artin representations to the Selmer coranks and their twists in the intermediate subextensions of thep-adic Lie extension.