Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields

In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary ℤ p -extension of a number field K in the case when p splits completely in K . Generalizing work of Kobayashi [ S. Kobayashi , Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152 (2003), no. 1, 1–36.] and Perrin-Riou [ B. Perrin-Riou , Arithmétique des courbes elliptiques á réduction supersingulière en p , Experiment. Math. 12 (2003), no. 2, 155–186.], we define restricted Selmer groups and λ ± , μ ± -invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic ℤ p -extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified ℤ p -extension of ℚ p .