ON IWASAWA THEORY OF ELLIPTIC CURVES OVER Q AT PRIMES OF SUPERSINGULAR REDUCTION 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 and Perrin-Riou , we define restricted Selmer groups and lambda(+/-), mu(+/-)-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).