The Iwasawa invariants of the plus/minus Selmer groups of elliptic curves for supersingular primes
نویسنده
چکیده
We study the Iwasawa μand λ-invariants of the plus/minus Selmer groups of elliptic curves with the same residual representation using the ideas of [8]. As a result we find a family of elliptic curves whose plus/minus Selmer groups have arbitrarily large λ-invariants.
منابع مشابه
Plus/minus Heegner Points and Iwasawa Theory of Elliptic Curves at Supersingular Primes
Let E be an elliptic curve over Q and let p ≥ 5 be a prime of good supersingular reduction for E. Let K be an imaginary quadratic field satisfying a modified “Heegner hypothesis” in which p splits, write K∞ for the anticyclotomic Zp-extension of K and let Λ denote the Iwasawa algebra of K∞/K. By extending to the supersingular case the Λ-adic Kolyvagin method originally developed by Bertolini in...
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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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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 ...
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At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is ...
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تاریخ انتشار 2008