Iwasawa Theory of Elliptic Curves at Supersingular Primes over Zp-extensions of Number Fields
نویسندگان
چکیده
In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Zp-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi [9] and Perrin-Riou [17], 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 Zp-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 Zp-extension of Qp.
منابع مشابه
2 2 N ov 2 00 4 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 Zp-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi [8] and Perrin-Riou [16], we define restricted Selmer groups and λ ± , µ ±-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in ter...
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