Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes
نویسندگان
چکیده
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...
متن کاملIwasawa 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 [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 ...
متن کاملThe main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
We develop the plus/minus p-Selmer group theory and plus/minus padic L-function theory for an elliptic curve E with complex multiplication over an abelian extension F of the imaginary quadratic field K given by the complex multiplication of E when p is a prime inert over K/Q (i.e. supersingular). As a result, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus p-Selm...
متن کاملThe Iwasawa invariants of the plus/minus Selmer groups of elliptic curves for supersingular primes
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.
متن کاملThe main conjecture for CM elliptic curves at supersingular primes
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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ژورنال
عنوان ژورنال: Bollettino dell'Unione Matematica Italiana
سال: 2018
ISSN: 1972-6724,2198-2759
DOI: 10.1007/s40574-018-0162-4