Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields

Details Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields

2004-11-22

arxiv.org/abs/math/0411496v1

Mathematics

Number Theory

35 pages

Scientific paper

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^\pm, \mu^\pm-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.

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