Adrian Iovita, Robert Pollack
Iwasawa theory of elliptic curves at supersingular primes over ℤp-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 [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 &lgr;±, 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.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 09/2006
Pages: 71 - 103
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