Signed-Selmer Groups over the ℤ²p-extension of an Imaginary Quadratic Field

Let E be an elliptic curve over ℚ that has good supersingular reduction at p > 3. We construct what we call the ±/±-Selmer groups of E over the ℤ 2 p -extension of an imaginary quadratic field K when the prime p splits completely over K / ℚ , and prove that they enjoy a property analogous to Mazur's control theorem. Furthermore, we propose a conjectural connection between the±/±-Selmer groups and Loeffler's two-variable ±/±- p -adic L -functions of elliptic curves.